In this paper, we present a general framework for low-level vision tasks including image compression artifacts reduction and image denoising. Under this framework, a novel concatenated attention neural network (CANet) is specifically designed for image restoration. The main contributions of this paper are as follows: First, by applying concise but effective concatenation and feature selection mechanism, we establish a novel connection mechanism which connect different modules in the modules stacking network. Second, both pixel-wise and channel-wise attention mechanisms are used in each module convolution layer, which promotes further extraction of more essential information in images. Lastly, we demonstrate that CANet achieves better results than previous state-of-the-art approaches with sufficient experiments in compression artifacts removing and image denoising.