With the advent of ever-growing vehicular applications, vehicular edge computing (VEC) has emerged as a solution to augment the computing capacity of future smart vehicles. However, the ultimate challenge of fulfilling quality of service (QoS) requirements becomes increasingly prominent due to the constrained computing and communication resources of vehicles. In this letter, we propose an energy-efficient task offloading scheme 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 the 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 mixed-integer and non-convex optimization problem is formulated and solved by adopting Lagrange dual problem. Via simulations, it is verified that the proposed method significantly reduces the vehicle's energy expenditure compared to the benchmark schemes.