diff --git a/src/ast/mod.rs b/src/ast/mod.rs
index 6a718702d..cf936d3c9 100644
--- a/src/ast/mod.rs
+++ b/src/ast/mod.rs
@@ -2728,11 +2728,17 @@ pub enum OnInsert {
 #[derive(Debug, Clone, PartialEq, PartialOrd, Eq, Ord, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub struct OnConflict {
-    pub conflict_target: Vec<Ident>,
+    pub conflict_target: Option<ConflictTarget>,
     pub action: OnConflictAction,
 }
 #[derive(Debug, Clone, PartialEq, PartialOrd, Eq, Ord, Hash)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
+pub enum ConflictTarget {
+    Columns(Vec<Ident>),
+    OnConstraint(ObjectName),
+}
+#[derive(Debug, Clone, PartialEq, PartialOrd, Eq, Ord, Hash)]
+#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub enum OnConflictAction {
     DoNothing,
     DoUpdate(DoUpdate),
@@ -2762,12 +2768,20 @@ impl fmt::Display for OnInsert {
 impl fmt::Display for OnConflict {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, " ON CONFLICT")?;
-        if !self.conflict_target.is_empty() {
-            write!(f, "({})", display_comma_separated(&self.conflict_target))?;
+        if let Some(target) = &self.conflict_target {
+            write!(f, "{}", target)?;
         }
         write!(f, " {}", self.action)
     }
 }
+impl fmt::Display for ConflictTarget {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match self {
+            ConflictTarget::Columns(cols) => write!(f, "({})", display_comma_separated(cols)),
+            ConflictTarget::OnConstraint(name) => write!(f, " ON CONSTRAINT {}", name),
+        }
+    }
+}
 impl fmt::Display for OnConflictAction {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         match self {
diff --git a/src/parser.rs b/src/parser.rs
index 26aa499e5..528b8c6fe 100644
--- a/src/parser.rs
+++ b/src/parser.rs
@@ -5630,7 +5630,15 @@ impl<'a> Parser<'a> {
             let on = if self.parse_keyword(Keyword::ON) {
                 if self.parse_keyword(Keyword::CONFLICT) {
                     let conflict_target =
-                        self.parse_parenthesized_column_list(IsOptional::Optional)?;
+                        if self.parse_keywords(&[Keyword::ON, Keyword::CONSTRAINT]) {
+                            Some(ConflictTarget::OnConstraint(self.parse_object_name()?))
+                        } else if self.peek_token() == Token::LParen {
+                            Some(ConflictTarget::Columns(
+                                self.parse_parenthesized_column_list(IsOptional::Mandatory)?,
+                            ))
+                        } else {
+                            None
+                        };
 
                     self.expect_keyword(Keyword::DO)?;
                     let action = if self.parse_keyword(Keyword::NOTHING) {
diff --git a/tests/sqlparser_postgres.rs b/tests/sqlparser_postgres.rs
index 5f178a91e..6b26fe48b 100644
--- a/tests/sqlparser_postgres.rs
+++ b/tests/sqlparser_postgres.rs
@@ -1112,12 +1112,12 @@ fn parse_pg_on_conflict() {
         Statement::Insert {
             on:
                 Some(OnInsert::OnConflict(OnConflict {
-                    conflict_target,
+                    conflict_target: Some(ConflictTarget::Columns(cols)),
                     action,
                 })),
             ..
         } => {
-            assert_eq!(vec![Ident::from("did")], conflict_target);
+            assert_eq!(vec![Ident::from("did")], cols);
             assert_eq!(
                 OnConflictAction::DoUpdate(DoUpdate {
                     assignments: vec![Assignment {
@@ -1142,15 +1142,12 @@ fn parse_pg_on_conflict() {
         Statement::Insert {
             on:
                 Some(OnInsert::OnConflict(OnConflict {
-                    conflict_target,
+                    conflict_target: Some(ConflictTarget::Columns(cols)),
                     action,
                 })),
             ..
         } => {
-            assert_eq!(
-                vec![Ident::from("did"), Ident::from("area"),],
-                conflict_target
-            );
+            assert_eq!(vec![Ident::from("did"), Ident::from("area"),], cols);
             assert_eq!(
                 OnConflictAction::DoUpdate(DoUpdate {
                     assignments: vec![
@@ -1183,12 +1180,11 @@ fn parse_pg_on_conflict() {
         Statement::Insert {
             on:
                 Some(OnInsert::OnConflict(OnConflict {
-                    conflict_target,
+                    conflict_target: None,
                     action,
                 })),
             ..
         } => {
-            assert_eq!(Vec::<Ident>::new(), conflict_target);
             assert_eq!(OnConflictAction::DoNothing, action);
         }
         _ => unreachable!(),
@@ -1204,12 +1200,49 @@ fn parse_pg_on_conflict() {
         Statement::Insert {
             on:
                 Some(OnInsert::OnConflict(OnConflict {
-                    conflict_target,
+                    conflict_target: Some(ConflictTarget::Columns(cols)),
+                    action,
+                })),
+            ..
+        } => {
+            assert_eq!(vec![Ident::from("did")], cols);
+            assert_eq!(
+                OnConflictAction::DoUpdate(DoUpdate {
+                    assignments: vec![Assignment {
+                        id: vec!["dname".into()],
+                        value: Expr::Value(Value::Placeholder("$1".to_string()))
+                    },],
+                    selection: Some(Expr::BinaryOp {
+                        left: Box::new(Expr::Identifier(Ident {
+                            value: "dsize".to_string(),
+                            quote_style: None
+                        })),
+                        op: BinaryOperator::Gt,
+                        right: Box::new(Expr::Value(Value::Placeholder("$2".to_string())))
+                    })
+                }),
+                action
+            );
+        }
+        _ => unreachable!(),
+    };
+
+    let stmt = pg_and_generic().verified_stmt(
+        "INSERT INTO distributors (did, dname, dsize) \
+        VALUES (5, 'Gizmo Transglobal', 1000), (6, 'Associated Computing, Inc', 1010)  \
+        ON CONFLICT ON CONSTRAINT distributors_did_pkey \
+        DO UPDATE SET dname = $1 WHERE dsize > $2",
+    );
+    match stmt {
+        Statement::Insert {
+            on:
+                Some(OnInsert::OnConflict(OnConflict {
+                    conflict_target: Some(ConflictTarget::OnConstraint(cname)),
                     action,
                 })),
             ..
         } => {
-            assert_eq!(vec![Ident::from("did")], conflict_target);
+            assert_eq!(vec![Ident::from("distributors_did_pkey")], cname.0);
             assert_eq!(
                 OnConflictAction::DoUpdate(DoUpdate {
                     assignments: vec![Assignment {