Integrating Multi-access Edge Computing (MEC) in Low Earth Orbit (LEO) network is an important way to provide glob-ally seamless low-delay service. In this paper, we consider the scenario that MEC platforms with computation and storage resource are deployed on LEO satellites, which is called LEO-MEC. Service request dispatching de-cision is very important for resource utilization of the whole LEO-MEC system and QoE of MEC users. Another important problem is ser-vice placement that is closely coupled with re-quest dispatching. This paper models the joint service request dispatching and service place-ment problem as an optimization problem, which is a Mixed Integer Linear Programming (MILP). Our proposed mechanism solves this problem and uses the solved decision variables to dispatch requests and place services. Simu-lation results show that our proposed mecha-nism can achieve better performance in terms of ratio of served users and average hop count compared with baseline mechanism.