Increasing reliance on large-scale AI models has led to rising demand for intelligent services. The centralized cloud computing approach has limitations in terms of data transfer efficiency and response time, and as a result many service providers have begun to deploy edge servers to cache intelligent services in order to reduce transmission delay and communication energy consumption. However, finding the optimal service caching strategy remains a significant challenge due to the stochastic nature of service requests and the bulky nature of intelligent services. To deal with this we propose a distributed service caching scheme integrating deep reinforcement learning (DRL) with mobility prediction, which we refer to as DSDM. Specifically, we employ the D3QN (Deep Double Dueling Q-Network) framework to integrate Long Short-Term Memory (LSTM) predicted mobile device locations into the service caching replacement algorithm and adopt the distributed multi-agent approach for learning and training. Experimental results demonstrate that DSDM achieves significant performance improvements in reducing communication energy consumption compared to traditional methods across various scenarios.