With the rapid growth of networked multimedia services in the Internet, wireless network traffic has increased dramatically. However, the current mainstream content caching schemes do not take into account the cooperation of different edge servers, resulting in deteriorated system performance. In this paper, we propose a learning-based edge caching scheme to enable mutual cooperation among different edge servers with limited caching resources, thus effectively reducing the content delivery latency. Specifically, we formulate the cooperative content caching problem as an optimization problem, which is proven to be NP-hard. To solve this problem, we design a new learning-based cooperative caching strategy (LECS) that encompasses three key components. Firstly, a temporal convolutional network driven content popularity prediction model is developed to estimate the content popularity with high accuracy. Secondly, with the predicted content popularity, the concept of content caching value (CCV) is introduced to weigh the value of a content cached on a given edge server. Thirdly, an novel dynamic programming algorithm is developed to maximize the overall CCV. Extensive simulation results have demonstrated the superiority of our approach. Compared with the state-of-the-art caching schemes, LECS can improve the cache hit rate by 8.3%-10.1%, and reduce the average content delivery delay by 9.1%-15.1%.