Edge computing is a novel network architecture that is in proximity to the end devices in an Internet of Things (IoT). As the IoT becoming a major factor in our daily life, provisioning a low response time of the services to IoT users through edge computing is an important problem. Caching necessary program data for the task in an edge node effectively reduces the response time of the computation task. However, due to the increase of IoT users and devices, it is noteworthy that limited-resource edge nodes would receive a number of tasks, having a heavy burden of processing the requests. Therefore, the limited resource and caching space at cloudlet need the careful design of the caching algorithm to utilize the space of multiple edge nodes and relieve the burden of computations. In this paper, we propose a cooperative program caching system that makes different edge nodes cooperatively store program data and cache the replicas of the data requested frequently to handle a number of requests from IoT users. In particular, we develop a cooperative caching algorithm that caches the appropriate number of data replicas depending on the number of requests on each cloudlet and the popularity of the data to minimize the response time. The simulation results show that the proposed cooperative caching algorithm can effectively reduce the response time for IoT users compared to other existing algorithms.