diff --git a/CHANGELOG.md b/CHANGELOG.md
index 009622afbf9..ad557c04537 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@
 * [#8862](https://github.com/rubocop-hq/rubocop/issues/8862): Fix an error for `Lint/AmbiguousRegexpLiteral` when using regexp without method calls in nested structure. ([@koic][])
 * [#8872](https://github.com/rubocop-hq/rubocop/issues/8872): Fix an error for `Metrics/ClassLength` when multiple assignments to constants. ([@koic][])
 * [#8871](https://github.com/rubocop-hq/rubocop/issues/8871): Fix a false positive for `Style/RedundantBegin` when using `begin` for method argument or part of conditions. ([@koic][])
+* [#8875](https://github.com/rubocop-hq/rubocop/issues/8875): Fix an incorrect auto-correct for `Style/ClassEqualityComparison` when comparing class name. ([@koic][])
 
 ## 0.93.0 (2020-10-08)
 
diff --git a/lib/rubocop/cop/style/class_equality_comparison.rb b/lib/rubocop/cop/style/class_equality_comparison.rb
index 57c3b533308..066a3221eef 100644
--- a/lib/rubocop/cop/style/class_equality_comparison.rb
+++ b/lib/rubocop/cop/style/class_equality_comparison.rb
@@ -21,7 +21,7 @@ class ClassEqualityComparison < Base
         include IgnoredMethods
         extend AutoCorrector
 
-        MSG = 'Use `Object.instance_of?` instead of comparing classes.'
+        MSG = 'Use `instance_of?(%<class_name>s)` instead of comparing classes.'
 
         RESTRICT_ON_SEND = %i[== equal? eql?].freeze
 
@@ -36,13 +36,28 @@ def on_send(node)
           return if def_node && ignored_method?(def_node.method_name)
 
           class_comparison_candidate?(node) do |receiver_node, class_node|
-            range = range_between(receiver_node.loc.selector.begin_pos, node.source_range.end_pos)
+            range = offense_range(receiver_node, node)
+            class_name = class_name(class_node, node)
 
-            add_offense(range) do |corrector|
-              corrector.replace(range, "instance_of?(#{class_node.source})")
+            add_offense(range, message: format(MSG, class_name: class_name)) do |corrector|
+              corrector.replace(range, "instance_of?(#{class_name})")
             end
           end
         end
+
+        private
+
+        def class_name(class_node, node)
+          if node.children.first.method?(:name)
+            class_node.source.delete('"').delete("'")
+          else
+            class_node.source
+          end
+        end
+
+        def offense_range(receiver_node, node)
+          range_between(receiver_node.loc.selector.begin_pos, node.source_range.end_pos)
+        end
       end
     end
   end
diff --git a/spec/rubocop/cop/style/class_equality_comparison_spec.rb b/spec/rubocop/cop/style/class_equality_comparison_spec.rb
index b0261adb1e1..d402e0df67c 100644
--- a/spec/rubocop/cop/style/class_equality_comparison_spec.rb
+++ b/spec/rubocop/cop/style/class_equality_comparison_spec.rb
@@ -5,21 +5,58 @@
     { 'IgnoredMethods' => [] }
   end
 
-  it 'registers an offense and corrects when comparing class for equality' do
+  it 'registers an offense and corrects when comparing class using `==` for equality' do
     expect_offense(<<~RUBY)
       var.class == Date
-          ^^^^^^^^^^^^^ Use `Object.instance_of?` instead of comparing classes.
+          ^^^^^^^^^^^^^ Use `instance_of?(Date)` instead of comparing classes.
+    RUBY
+
+    expect_correction(<<~RUBY)
+      var.instance_of?(Date)
+    RUBY
+  end
+
+  it 'registers an offense and corrects when comparing class using `equal?` for equality' do
+    expect_offense(<<~RUBY)
       var.class.equal?(Date)
-          ^^^^^^^^^^^^^^^^^^ Use `Object.instance_of?` instead of comparing classes.
+          ^^^^^^^^^^^^^^^^^^ Use `instance_of?(Date)` instead of comparing classes.
+    RUBY
+
+    expect_correction(<<~RUBY)
+      var.instance_of?(Date)
+    RUBY
+  end
+
+  it 'registers an offense and corrects when comparing class using `eql?` for equality' do
+    expect_offense(<<~RUBY)
       var.class.eql?(Date)
-          ^^^^^^^^^^^^^^^^ Use `Object.instance_of?` instead of comparing classes.
+          ^^^^^^^^^^^^^^^^ Use `instance_of?(Date)` instead of comparing classes.
+    RUBY
+
+    expect_correction(<<~RUBY)
+      var.instance_of?(Date)
     RUBY
   end
 
-  it 'registers an offense and corrects when comparing class name for equality' do
+  it 'registers an offense and corrects when comparing single quoted class name for equality' do
+    expect_offense(<<~RUBY)
+      var.class.name == 'Date'
+          ^^^^^^^^^^^^^^^^^^^^ Use `instance_of?(Date)` instead of comparing classes.
+    RUBY
+
+    expect_correction(<<~RUBY)
+      var.instance_of?(Date)
+    RUBY
+  end
+
+  it 'registers an offense and corrects when comparing double quoted class name for equality' do
     expect_offense(<<~RUBY)
       var.class.name == "Date"
-          ^^^^^^^^^^^^^^^^^^^^ Use `Object.instance_of?` instead of comparing classes.
+          ^^^^^^^^^^^^^^^^^^^^ Use `instance_of?(Date)` instead of comparing classes.
+    RUBY
+
+    expect_correction(<<~RUBY)
+      var.instance_of?(Date)
     RUBY
   end