Mobile Edge Computing (MEC) provides an effective solution to the conflict between computationally intensive applications and resource constrained mobile devices. However, most studies on the MEC offloading only consider the resource allocation between mobile devices and MEC servers, and ignore the huge computing resources in the cloud computing centers. In order to make full use of cloud and MEC resources, a task offloading strategy of cloud-edge collaboration was proposed. Firstly, the task offloading problem of the cloud-edge servers was transformed into a game problem. Then, the existence and uniqueness of Nash Equilibrium (NE) in this game were proved, and the solution to this game problem was obtained. Finally, a two-stage task offloading algorithm based on game theory was proposed to solve the task offloading scheme, and the performance of this algorithm was evaluated by performance indicators. The simulation results show that the total overhead of using the proposed algorithm is reduced by 72.8%, 47.9%, and 2.65% compared with those of local execution, cloud server execution and MEC server execution, respectively. The numerical results confirm that the proposed strategy can achieve higher energy efficiency and lower task offloading overhead, and extend scale well with the number of mobile devices increases.