Edge computing is an emerging computational model that enables efficient offloading of service requests to edge servers. By leveraging the well-developed technologies of cloud computing, the computing capabilities of mobile devices can be significantly enhanced in edge computing paradigm. However, upon the arrival of user requests, whether to dispatch them to the edge servers or cloud servers in order to guarantee the quality of service (QoS), i.e., the QoS-aware service selection problem, still remains an open problem. Due to the dynamic mobility of users and the variation of task arrivals and service processes, it is extremely costly to obtain the global optimal solution by both mathematical approaches and simulation-based schemes. To attack this challenge, this paper proposes a simulation-based approach of QoS-aware dynamic service selection for mobile edge computing systems. Stochastic system models are presented and mathematical analyses are provided. Based on the analytical results, the QoS-aware service selection problem is formulated by a dynamic optimization problem. Goal softening is applied to the original problem, and service selection algorithms are designed using ordinal optimization techniques. Simulation experiments are conducted to validate the efficacy of the approach presented in this paper.