With the development of the Internet of Things (IoT) and 5G/6G technologies, there has been significant interest in the applications of the Internet of Vehicles (IoV) and multiaccess edge computing (MEC) in intelligent transportation systems. The significant increase in the number of vehicles currently accessing the Internet has highlighted the inability of some existing resource-constrained vehicles to adequately meet the demands of computationally intensive and latency-sensitive applications. There is a significant challenge in designing efficient task offloading strategies to enhance the utilization of computational resources and deliver high-quality services to vehicle users. In this article, we propose a four-tier computing architecture with local computing, vehicle-to-vehicle (V2V) computing, MEC computing, and mobile cloud computing (MCC), which can provide heterogeneous computing resources for multiple task vehicles and flexible offloading options of different types of vehicle tasks. We optimize the offloading decision and resource allocation with the objective function of minimizing the system cost. The nonconvex objective function and constraints both contain binary variables, which leads to NP-hard property. To solve this critical problem, we propose an alternating direction method of multipliers (ADMM)-based multivehicle task offloading scheme for IoV-MEC (AMTOS), to transform the nonconvex problem into a convex one by relaxing the binary variables, and provide an approximate optimal solution. Afterward, a binary variable recovery algorithm is used to recover the binary variables. Simulation results show that the algorithm can significantly reduce the system cost, compared with existing literature.