With the proliferation of mobile applications, Mobile Cloud Computing (MCC) has been proposed to help mobile devices save energy and improve computation performance. To further improve the quality of service (QoS) of MCC, cloud servers can be deployed locally so that the latency is decreased. However, the computational resource of the local cloud is generally limited. In this paper, we design a threshold-based policy to improve the QoS of MCC by cooperation of the local cloud and Internet cloud resources, which takes the advantages of low latency of the local cloud and abundant computational resources of the Internet cloud simultaneously. This policy also applies a priority queue in terms of delay requirements of applications. The optimal thresholds depending on the traffic load is obtained via a proposed algorithm. Numerical results show that the QoS can be greatly enhanced with the assistance of Internet cloud when the local cloud is overloaded. Better QoS is achieved if the local cloud order tasks according to their delay requirements, where delay-sensitive applications are executed ahead of delay-tolerant applications. Moreover, the optimal thresholds of the policy have a sound impact on the QoS of the system.