With the advent of ever-growing vehicular applications, vehicular edge computing (VEC) has been a promising solution to augment the computing capacity of future smart vehicles. The ultimate challenge to fulfill the quality of service (QoS) is increasingly prominent with constrained computing and communication resources of vehicles. In this paper, we propose an energy-efficient task offloading strategy for VEC system with one-by-one scheduling mechanism, where only one vehicle wakes up at a time to offload with a road side unit (RSU). The goal of system is to minimize the total energy consumption of vehicles by jointly optimizing user scheduling, offloading ratio and bit allocation within a given mission time. To this end, the non-convex and mixed-integer optimization problem is formulated and solved by adopting Lagrange dual problem, whose superior performances are verified via numerical results, as compared to other benchmark schemes.