Blocking artifact, characterized by visually noticeable changes in pixel values along block boundaries, is a general problem in block-based image/video compression systems. Various post-processing techniques have been proposed to reduce blocking artifacts, but most of them usually introduce excessive blurring or ringing effects. This paper presents a deep learning-based compression artifacts reduction (or deblocking) framework relying on multi-scale residual learning. Recent popular approaches usually train deep models using a per-pixel loss function with explicit image priors for directly producing deblocked images. Instead, we formulate the problem as learning the residuals (or the artifacts) between original and the corresponding compressed images. In our deep model, each input image is down-scaled first with blocking artifacts naturally reduced. Then, the learned SR (super-resolution) convolutional neural network (CNN) will be used to up-sample the down-scaled version. Finally, the up-scaled version (with less artifacts) and the original input are fed into the learned artifact prediction CNN to obtain the estimated blocking artifacts. As a result, the blocking artifacts can be successfully removed by subtracting the predicted artifacts from the input image while preserving most original visual details.