Many studies have been conducted so far on image restoration, the problem of restoring a clean image from its distorted version. There are many different types of distortion affecting image quality. Previous studies have focused on single types of distortion, proposing methods for removing them. However, image quality degrades due to multiple factors in the real world. Thus, depending on applications, e.g., vision for autonomous cars or surveillance cameras, we need to be able to deal with multiple combined distortions with unknown mixture ratios. For this purpose, we propose a simple yet effective layer architecture of neural networks. It performs multiple operations in parallel, which are weighted by an attention mechanism to enable selection of proper operations depending on the input. The layer can be stacked to form a deep network, which is differentiable and thus can be trained in an end-to-end fashion by gradient descent. The experimental results show that the proposed method works better than previous methods by a good margin on tasks of restoring images with multiple combined distortions.