The increasing number of smart vehicles and their resource hungry applications pose new challenges in terms of computation and processing for providing reliable and efficient vehicular services. Mobile Edge Computing (MEC) is a new paradigm with potential to improve vehicular services through computation offloading in close proximity to mobile vehicles. However, in the road with dense traffic flow, the computation limitation of these MEC servers may endanger the quality of offloading service. To address the problem, we propose a hierarchical cloud-based Vehicular Edge Computing (VEC) offloading framework, where a backup computing server in the neighborhood is introduced to make up for the deficit computing resources of MEC servers. Based on this framework, we adopt a Stackelberg game theoretic approach to design an optimal multilevel offloading scheme, which maximizes the utilities of both the vehicles and the computing servers. Furthermore, to obtain the optimal offloading strategies, we present an iterative distributed algorithm and prove its convergence. Numerical results indicate that our proposed scheme greatly enhances the utility of the offloading service providers.