Taking into consideration of vehicle mobility and fairness, in this paper we provide a cooperative offloading algorithm maximizing the energy efficiency for a vehicular edge computing network, while guaranteeing the shortest delay of the worst-case vehicle. In particular, through exploiting the geometrical feature of the unidirectional road, we formulate a mixed integer convex problem by jointly designing the offloading selection and allocating the computation resource simultaneously. The optimization is carried out by a proposed two-step optimization algorithm: We first optimize the server selection to obtain the minimized achievable delay, and subsequently optimize jointly the selection and resource allocation to maximize the energy efficiency while maintaining the optimal achievable delay. Via simulations, we show the advantage of proposed algorithms and evaluate the system performance.