Edge caching can effectively reduce service latency, alleviate backhaul traffic pressure, and enhance the quality of experience (QoE) through the reuse of popular network content. Many studies utilize deep reinforcement learning (DRL) methods to learn optimal caching strategies for mobile edge networks. However, traditional DRL methods often suffer from limitations such as inefficient sample utilization, lengthy training periods, and insufficient model generalization performance, which necessitate relearning network parameters when faced with new tasks. To overcome these challenges, this paper proposes a meta-reinforcement learning based fast adaptive edge caching algorithm (MRFAC). It models the mobile edge caching problem as a markov decision process (MDP) and designs a DRL algorithm to optimize the cache replacement strategy, aiming to maximize long-term caching benefits. Moreover, meta-learning is incorporated into DRL algorithm, treating the learning process of DRL as an independent learning objective. The weights of the gated recurrent unit (GRU) are used to encode and store the learned prior knowledge, enabling MRFAC to rapidly adapt to new tasks. Experiment results indicate that the cache performance of MRFAC outperforms baseline methods such as LFU, FIFO, and DDPG. Furthermore, MRFAC exhibits rapid adaptation to new tasks, with significantly improved convergence speed compared to traditional DRL methods.