The precise prediction of ship fuel consumption (SFC) not only serves to enhance energy efficiency to benefit shipping enterprises but also to provide quantitative foundations to aid in carbon emission reduction and ecological environment protection. On the other hand, SFC-related data represent typical multi-source characteristics and heterogeneous features, which lead to several methodological issues (e.g., feature alignment and feature fusion) in SFC prediction. Therefore, this paper proposes a dual-attention parallel network named DAPNet to solve the above issues. Firstly, we design a parallel network structure containing two kinds of long short-term memory (LSTM) and improved temporal convolutional networks (TCNs) for time-series analysis tasks so that different source data can be applied to suitable networks. Secondly, a local attention mechanism is included in each single parallel network so as to improve the ability of feature alignment from different-scale training data. Finally, global attention is employed for the fusion of all parallel networks, which can enrich representation features and simultaneously enhance the performance of SFC prediction. In experiments, DAPNet is compared with 10 methods, including baseline and attention models. The comparison results show that DAPNet and several of its variants obtain the highest accuracy in SFC prediction.