diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4a358f996e..be7f7d55f4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,9 +7,9 @@
 #### Fixes
 
 * [#1740](/~https://github.com/ruby-grape/grape/pull/1740): Fix dependent parameter validation using `given` when parameter is a `Hash` - [@jvortmann](/~https://github.com/jvortmann).
-
-* Your contribution here.
 * [#1737](/~https://github.com/ruby-grape/grape/pull/1737): Fix translating error when passing symbols as params in custom validations - [@mlzhuyi](/~https://github.com/mlzhuyi).
+* [#1749](/~https://github.com/ruby-grape/grape/pull/1749): Allow rescue from non-`StandardError` errors - [@dm1try](/~https://github.com/dm1try).
+* Your contribution here.
 
 ### 1.0.2 (1/10/2018)
 
diff --git a/README.md b/README.md
index 9e70ddd8c1..6635909eff 100644
--- a/README.md
+++ b/README.md
@@ -78,6 +78,7 @@
 - [Exception Handling](#exception-handling)
     - [Rescuing exceptions inside namespaces](#rescuing-exceptions-inside-namespaces)
     - [Unrescuable Exceptions](#unrescuable-exceptions)
+    - [Exceptions that should be rescued explicitly](#exceptions-that-should-be-rescued-explicitly)
   - [Rails 3.x](#rails-3x)
 - [Logging](#logging)
 - [API Formats](#api-formats)
@@ -2079,6 +2080,9 @@ class Twitter::API < Grape::API
 end
 ```
 
+This mimics [default `rescue` behaviour](https://ruby-doc.org/core/StandardError.html) when an exception type is not provided.
+Any other exception should be rescued explicitly, see [below](#exceptions-that-should-be-rescued-explicitly).
+
 Grape can also rescue from all exceptions and still use the built-in exception handing.
 This will give the same behavior as `rescue_from :all` with the addition that Grape will use the exception handling defined by all Exception classes that inherit `Grape::Exceptions::Base`.
 
@@ -2281,6 +2285,12 @@ Here `'inner'` will be result of handling occured `ArgumentError`.
 
 `Grape::Exceptions::InvalidVersionHeader`, which is raised when the version in the request header doesn't match the currently evaluated version for the endpoint, will _never_ be rescued from a `rescue_from` block (even a `rescue_from :all`) This is because Grape relies on Rack to catch that error and try the next versioned-route for cases where there exist identical Grape endpoints with different versions.
 
+#### Exceptions that should be rescued explicitly
+
+Any exception that is not subclass of `StandardError` should be rescued explicitly.
+Usually it is not a case for an application logic as such errors point to problems in Ruby runtime.
+This is following [standard recomendations for exceptions handling](https://ruby-doc.org/core/Exception.html)
+
 ### Rails 3.x
 
 When mounted inside containers, such as Rails 3.x, errors such as "404 Not Found" or
diff --git a/lib/grape/middleware/error.rb b/lib/grape/middleware/error.rb
index 3c00786bfd..bdb0b073c7 100644
--- a/lib/grape/middleware/error.rb
+++ b/lib/grape/middleware/error.rb
@@ -46,6 +46,14 @@ def call!(env)
           end
 
           handler.nil? ? handle_error(e) : exec_handler(e, &handler)
+        rescue Exception => e # rubocop:disable Lint/RescueException
+          handler = options[:rescue_handlers].find do |error_class, error_handler|
+            break error_handler if e.class <= error_class
+          end
+
+          raise unless handler
+
+          exec_handler(e, &handler)
         end
       end
 
diff --git a/spec/grape/middleware/exception_spec.rb b/spec/grape/middleware/exception_spec.rb
index e6bb44597b..54df280fe4 100644
--- a/spec/grape/middleware/exception_spec.rb
+++ b/spec/grape/middleware/exception_spec.rb
@@ -109,6 +109,19 @@ def app
     end
   end
 
+  context 'Non-StandardError exception with a provided rescue handler' do
+    subject do
+      Rack::Builder.app do
+        use Spec::Support::EndpointFaker
+        use Grape::Middleware::Error, rescue_handlers: { NotImplementedError => -> { [200, {}, 'rescued'] } }
+        run ExceptionSpec::OtherExceptionApp
+      end
+    end
+    it 'rescues the exception using the provided handler' do
+      get '/'
+      expect(last_response.body).to eq('rescued')
+    end
+  end
   context do
     subject do
       Rack::Builder.app do