In this paper, we propose a hierarchical Stackelberg game based resource allocation algorithm (HGRAA) to jointly allocate the wireless and computational resources of a mobile edge computing (MEC) system. The proposed HGRAA is composed of two levels: the lower-level evolutionary game (LEG) minimizes the cost of mobile terminals (MTs), and the upper-level exact potential game (UEPG) maximizes the utility of MEC servers. At the lower-level, the MTs are divided into delay-sensitive MTs (DSMTs) and non-delay-sensitive MTs (NDSMTs) according to their different quality of service (QoS) requirements. The competition among DSMTs and NDSMTs in different service areas to share the limited available wireless and computational resources is formulated as a dynamic evolutionary game. The dynamic replicator is applied to obtain the evolutionary equilibrium so as to minimize the costs imposed on MTs. At the upper level, the exact potential game is formulated to solve the resource sharing problem among MEC servers and the resource sharing problem is transferred to nonlinear complementarity. The existence of Nash equilibrium (NE) is proved and is obtained through the Karush-Kuhn-Tucker (KKT) condition. Simulations illustrate that substantial performance improvements such as average utility and the resource utilization of MEC servers can be achieved by applying the proposed HGRAA. Moreover, the cost of MTs is significantly lower than other existing algorithms with the increasing size of input data, and the QoS requirements of different kinds of MTs are well guaranteed in terms of average delay and transmission data rate.