A deep neural network is difficult to train due to a large number of unknown parameters. To increase trainable performance, we present a moderate depth residual network for the restoration of motion blurring and noisy images. The proposed network has only 10 layers, and the sparse feedbacks are added in the middle and the last layers, which are called FbResNet. FbResNet has fast convergence speed and effective denoising performance. In addition, it can also reduce the artificial Mosaic trace at the seam of patches, and visually pleasant output results can be produced from the blurred images or noisy images. Experimental results show the effectiveness of our designed model and method.