diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0b646c7fd58..05b88f3ebc0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -16,6 +16,7 @@
 
 * [#8646](https://github.com/rubocop-hq/rubocop/issues/8646): Faster find of all files in `TargetFinder` class which improves initial startup speed. ([@tleish][])
 * [#8102](https://github.com/rubocop-hq/rubocop/issues/8102): Consider class length instead of block length for `Struct.new`. ([@tejasbubane][])
+* [#7408](https://github.com/rubocop-hq/rubocop/issues/7408): Make `Gemspec/RequiredRubyVersion` cop aware of `Gem::Requirement`. ([@tejasbubane][])
 
 ## 0.92.0 (2020-09-25)
 
diff --git a/lib/rubocop/cop/gemspec/required_ruby_version.rb b/lib/rubocop/cop/gemspec/required_ruby_version.rb
index aeed941b855..7b912b48257 100644
--- a/lib/rubocop/cop/gemspec/required_ruby_version.rb
+++ b/lib/rubocop/cop/gemspec/required_ruby_version.rb
@@ -58,24 +58,22 @@ class RequiredRubyVersion < Cop
           (send _ :required_ruby_version= $_)
         PATTERN
 
-        def_node_matcher :string_version?, <<~PATTERN
-          {(str _) (array (str _))}
+        def_node_matcher :defined_ruby_version, <<~PATTERN
+          {$(str _) $(array (str _) (str _))
+            (send (const (const nil? :Gem) :Requirement) :new $(str _))}
         PATTERN
 
         # rubocop:disable Metrics/AbcSize
         def investigate(processed_source)
-          version = required_ruby_version(processed_source.ast).first
+          version_def = required_ruby_version(processed_source.ast).first
 
-          if version
-            return unless string_version?(version)
-
-            ruby_version = extract_ruby_version(version)
-
-            return if ruby_version == target_ruby_version.to_s
+          if version_def
+            ruby_version = extract_ruby_version(defined_ruby_version(version_def))
+            return if !ruby_version || ruby_version == target_ruby_version.to_s
 
             add_offense(
               processed_source.ast,
-              location: version.loc.expression,
+              location: version_def.loc.expression,
               message: not_equal_message(ruby_version, target_ruby_version)
             )
           else
@@ -88,6 +86,8 @@ def investigate(processed_source)
         private
 
         def extract_ruby_version(required_ruby_version)
+          return unless required_ruby_version
+
           if required_ruby_version.array_type?
             required_ruby_version = required_ruby_version.children.detect do |v|
               /[>=]/.match?(v.str_content)
diff --git a/spec/rubocop/cop/gemspec/required_ruby_version_spec.rb b/spec/rubocop/cop/gemspec/required_ruby_version_spec.rb
index 789df4a1f07..4c3f2c49fe6 100644
--- a/spec/rubocop/cop/gemspec/required_ruby_version_spec.rb
+++ b/spec/rubocop/cop/gemspec/required_ruby_version_spec.rb
@@ -20,6 +20,24 @@
       RUBY
     end
 
+    it 'registers an offense when `required_ruby_version` is specified in array and is lower than `TargetRubyVersion`' do
+      expect_offense(<<~RUBY, '/path/to/foo.gemspec')
+        Gem::Specification.new do |spec|
+          spec.required_ruby_version = ['>= 2.6.0', '< 3.0.0']
+                                       ^^^^^^^^^^^^^^^^^^^^^^^ `required_ruby_version` (2.6, declared in foo.gemspec) and `TargetRubyVersion` (2.7, which may be specified in .rubocop.yml) should be equal.
+        end
+      RUBY
+    end
+
+    it 'recognizes Gem::Requirement and registers offense' do
+      expect_offense(<<~RUBY, '/path/to/foo.gemspec')
+        Gem::Specification.new do |spec|
+          spec.required_ruby_version = Gem::Requirement.new(">= 2.6.0")
+                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ `required_ruby_version` (2.6, declared in foo.gemspec) and `TargetRubyVersion` (2.7, which may be specified in .rubocop.yml) should be equal.
+        end
+      RUBY
+    end
+
     describe 'false negatives' do
       it 'does not register an offense when `required_ruby_version` ' \
          'is assigned as a variable (string literal)' do