Duplicated download has been a big problem that affects the users' quality of service/experience (QoS/QoE) of current mobile networks. Edge caching and Device-to-Device communication are two promising technologies to release the pressure of repeated traffic downloading from the cloud. There are many researches about the edge caching policy. However, these researches have some limitations in the real scenarios. Traditional methods are lacking the self-adaptive ability in the dynamic environment and privacy issues will occur in centralized learning methods. In this paper, based on the virtue of Deep Q-Network (DQN), we propose a weighted distributed DQN model (WDDQN) to solve the cache replacement problem. Our model enables collaboratively to learn a shared predictive model. Trace-driven simulation results show that our proposed model outperforms some classical and state-of-the-art schemes.