Different from cloud computing, edge computing moves computing away from the centralized data center and closer to the end-user. Therefore, with the large-scale deployment of edge services, it becomes a new challenge of how to dynamically select the appropriate edge server for computing requesters based on the edge server and network status. In the TCP/IP architecture, edge computing applications rely on centralized proxy servers to select an appropriate edge server, which leads to additional network overhead and increases service response latency. Due to its powerful forwarding plane, Information-Centric Networking (ICN) has the potential to provide more efficient networking support for edge computing than TCP/IP. However, traditional ICN only addresses named data and cannot well support the handle of dynamic content. In this article, we propose an edge computing service architecture based on ICN, which contains the edge computing service session model, service request forwarding strategies, and service dynamic deployment mechanism. The proposed service session model can not only keep the overhead low but also push the results to the computing requester immediately once the computing is completed. However, the service request forwarding strategies can forward computing requests to an appropriate edge server in a distributed manner. Compared with the TCP/IP-based proxy solution, our forwarding strategy can avoid unnecessary network transmissions, thereby reducing the service completion time. Moreover, the service dynamic deployment mechanism decides whether to deploy an edge service on an edge server based on service popularity, so that edge services can be dynamically deployed to hotspot, further reducing the service completion time.