Convolution neural network (CNN) has been widely used in the field of remaining useful life (RUL) prediction. However, the CNN-based RUL prediction methods have some limitations. The receptive field of CNN is limited and easy to happen gradient vanishing problem when the network is too deep. The contribution differences of different channels and different time steps to RUL prediction are not considered, and only use deep learning features or handcrafted statistical features for prediction. These limitations can lead to inaccurate prediction results. To solve these problems, this paper proposes an RUL prediction method based on multi-layer self-attention (MLSA) and temporal convolution network (TCN). The TCN is used to extract deep learning features. Dilated convolution and residual connection are adopted in TCN structure. Dilated convolution is an efficient way to widen receptive field, and the residual structure can avoid the gradient vanishing problem. Besides, we propose a feature fusion method to fuse deep learning features and statistical features. And the MLSA is designed to adaptively assign feature weights. Finally, the turbofan engine dataset is used to verify the proposed method. Experimental results indicate the effectiveness of the proposed method.