The conventional methods for the next-item recommendation are generally based on RNN or one-dimensional attention with time encoding. They are either hard to preserve the long-term dependencies between different interactions, or hard to capture fine-grained user preferences. In this paper, we propose a Double Most Relevant Attention Network (DMRAN) that contains two layers, i.e., Item level Attention and Feature Level Self-attention, which are to pick out the most relevant items from the sequence of user's historical behaviors, and extract the most relevant aspects of relevant items, respectively. Then, we can capture the fine-grained user preferences to better support the next-item recommendation. Extensive experiments on two real-world datasets illustrate that DMRAN can improve the efficiency and effectiveness of the recommendation compared with the state-of-the-art methods.