Optical remote-sensing images have a wide range of applications, but they are often obscured by clouds, which affects subsequent analysis. Therefore, cloud removal becomes a necessary preprocessing step. In this paper, a novel and superior transformer-based network is proposed, named Cloudformer. The proposed method novelly combines the advantages of convolution and a self-attention mechanism: it uses convolution layers to extract simple features over a small range in the shallow layer, and exerts the advantage of a self-attention mechanism in extracting correlation in a large range in the deep layer. This method also introduces Locally-enhanced Positional Encoding (LePE) to flexibly generate suitable positional encodings for different inputs and to utilize local information to enhance encoding capabilities. Exhaustive experiments on public datasets demonstrate the superior ability of the method to remove both thin and thick clouds, and the effectiveness of the proposed modules is validated by ablation studies.