While the multi-branch architecture is one of the key ingredients to the success of computer vision tasks, it has not been well investigated in natural language processing, especially sequence learning tasks. In this work, we propose a simple yet effective variant of Transformer called multi-branch attentive Transformer (briefly, MAT), where the attention layer is the average of multiple branches and each branch is an independent multi-head attention layer. We leverage two training techniques to regularize the training: drop-branch, which randomly drops individual branches during training, and proximal initialization, which uses a pre-trained Transformer model to initialize multiple branches. Experiments on machine translation, code generation and natural language understanding demonstrate that such a simple variant of Transformer brings significant improvements. Our code is available at url{https://github.com/HA-Transformer}.