Modern remote sensing (RS) image application systems often distribute image processing tasks among multiple data centers and then gather the processed images from each center to efficiently synthesize the final product. In this paper, we exploit the edge-cloud architecture to design and implement a novel RS image service system, called RS-pCloud, which leverages the Peer-to-Peer (P2P) model to integrate multiple data centers and their associated edge networks. The data center as cloud platform is responsible for the storage and processing of original RS images, as well as the storage of partial processed images while the edge network is mainly for caching and sharing the processed images. With this design, RS-pCloud not only achieves the load sharing of processing works but also attains the data efficiency among the edges at the same time, which in turn improves the performance of the image processing and reduce the cost of the data transmission as well. RS-pCloud is designed to be used in a transparent way where it receives a query task from the user through a certain cloud platform, split the task into different sub-tasks, according to the location of the data they required, and then distribute the sub-tasks to corresponding clouds for near-data processing, the returned results from each cloud are first cached in specific edge for further sharing and then gathered at the client to synthesize the final product. We implemented and deployed RS-pCloud on three clusters in conjunction with an edge network to show its performance advantages over traditional single-cluster systems.