In mobile edge computing, cloudlets can provide cloud services for mobile users in specific areas. Considering that users movements can be viewed as stochastic processes, it is hard to make migration decisions optimally due to a large number of system states. Meanwhile, how to minimize service cost of cloudlets with delay constraint is an NP-hard problem. In this paper, we formulate the issue of service migration with delay constraint as a Markov decision process (MDP) and propose a reinforcement learning based service migration strategy to reduce service cost. The experimental results show that our proposed solution achieves a better tradeoff between service cost and delay compared to other existing strategies.