With the proliferation of smartphones and an increasing number of services provisioned by clouds, mobile edge computing (MEC) is emerging as a complementary technology of cloud computing. It could provide cloud resources and services by local mobile edge servers, which are normally nearby users. However, a significant challenge is aroused in MEC because of the mobility of users. User trajectory prediction technologies could be used to cope with this issue, which has already played important roles in service recommendation systems with MEC. Unfortunately, little attention and work have been given in service recommendation systems considering users mobility. Thus, in this paper, we propose a mobility-aware personalized service recommendation (MPSR) approach based on user trajectory and quality of service (QoS) predictions. In the proposed method, users trajectory is firstly discovered by a hybrid long-short memory network. Then, given users trajectories, service QoS is predicted, considering the similarity of different users and different edge servers. Finally, services are recommended by a center trajectory strategy through MPSR. Experimental results on a real dataset show that our proposed approach can outperform the traditional recommendation approaches in terms of accuracy in mobile edge computing.