diff --git a/modules/dnn/src/onnx/onnx_importer.cpp b/modules/dnn/src/onnx/onnx_importer.cpp
index ccef2f6936..8cb2c5eda1 100644
--- a/modules/dnn/src/onnx/onnx_importer.cpp
+++ b/modules/dnn/src/onnx/onnx_importer.cpp
@@ -946,6 +946,19 @@ void ONNXImporter::populateNet(Net dstNet)
                 Mat bias = getBlob(node_proto, constBlobs, 2);
                 layerParams.blobs.push_back(bias);
             }
+            if (constBlobs.find(node_proto.input(0)) != constBlobs.end())
+            {
+                Mat inputBuf = getBlob(node_proto, constBlobs, 0);
+
+                LayerParams constParams;
+                constParams.name = node_proto.input(0);
+                constParams.type = "Const";
+                constParams.blobs.push_back(inputBuf);
+
+                opencv_onnx::NodeProto proto;
+                proto.add_output(constParams.name);
+                addLayer(dstNet, constParams, proto, layer_id, outShapes);
+            }
 
             layerParams.set("num_output", layerParams.blobs[0].size[ind_num_out]);
             layerParams.set("bias_term", node_proto.input_size() == 3);
diff --git a/modules/dnn/test/test_onnx_importer.cpp b/modules/dnn/test/test_onnx_importer.cpp
index c68215ee30..1eb848897c 100644
--- a/modules/dnn/test/test_onnx_importer.cpp
+++ b/modules/dnn/test/test_onnx_importer.cpp
@@ -611,6 +611,26 @@ TEST_P(Test_ONNX_layers, Pad2d_Unfused)
     testONNXModels("ZeroPad2d");
 }
 
+TEST_P(Test_ONNX_layers, LinearWithConstant)
+{
+    if (backend == DNN_BACKEND_OPENCV && target == DNN_TARGET_OPENCL_FP16)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL_FP16);
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2020040000)
+    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE);
+#endif
+    testONNXModels("lin_with_constant");
+}
+
+TEST_P(Test_ONNX_layers, MatmulWithTwoInputs)
+{
+    if (backend == DNN_BACKEND_OPENCV && target == DNN_TARGET_OPENCL_FP16)
+        applyTestTag(CV_TEST_TAG_DNN_SKIP_OPENCL_FP16);
+#if defined(INF_ENGINE_RELEASE) && INF_ENGINE_VER_MAJOR_LT(2020040000)
+    applyTestTag(CV_TEST_TAG_DNN_SKIP_IE);
+#endif
+    testONNXModels("matmul_with_two_inputs");
+}
+
 INSTANTIATE_TEST_CASE_P(/*nothing*/, Test_ONNX_layers, dnnBackendsAndTargets());
 
 class Test_ONNX_nets : public Test_ONNX_layers