Mobile edge computing (MEC) reduces data service latency by pushing data to the network edge. However, due to the dynamic and diverse requests of mobile users, the problem of mobile edge caching is more complex than cloud caching. Therefore, the existing model-based caching strategies cannot be directly used in the mobile edge caching environment. Besides, when taking the cooperative storage relationship between neighbor edge servers into consideration, the caching problem becomes more difficult. To this end, we formulate an mobile edge caching problem to minimize the total latency in mobile edge computing. Firstly, a heuristic caching strategy is proposed to solve the mobile edge caching problem in the single-time-slot scenario. Then, with the consideration of users’ mobility and the correlation of files, we propose a caching strategy for the multiple-time-slot scenario based on multi-agent deep reinforcement learning. To address the cold start problem in deep reinforcement learning, we adopt the proposed heuristic caching strategy used in the single-time-slot scenario to further optimize the training results. Extensive experiments on generated data and real-world datasets are conducted to verify that the proposed edge caching strategies can achieve the minimum latency compared with the state-of-the-art strategies.