Vehicular edge computing (VEC) is a potential field that distributes computational tasks between VEC servers and local vehicular terminals, hence improve vehicular services. At present, vehicles’ intelligence and capabilities are rapidly improving, which will likely support many new and exciting applications. The network resources are well-utilized by exploiting neighboring vehicles’ available resources while mitigating the VEC server’s heavy burden. However, due to the vehicles’ mobility, network topology, and the available computing resources change rapidly, which are difficult to predict. To tackle this problem, we investigate the task offloading schemes by utilizing vehicle to vehicle and vehicle to infrastructure communication modes and exploiting the vehicle’s under-utilized computation and communication resources, and taking the cost and time consumption into account. We present a promising relay task-offloading scheme in vehicular edge computing (RVEC). According to this scheme, the tasks are offloaded in a vehicle to vehicle relay for computation while being transmitted to VEC servers. Numerical results illustrate that the RVEC scheme substantially enhances the network’s overall offloading cost.