With the development of 5G technology, the requirements for data communication and computation in emerging 5G-enabled vehicular networks are becoming increasingly stringent. Computation-intensive or delay-sensitive tasks generated by vehicles need to be processed in real time. Mobile edge computing (MEC) is an appropriate solution. Wireless users or vehicles can offload computation tasks to the MEC server due to it has strong computation ability and is closer to the wireless users or vehicles. However, the communication and computation resources of the single MEC are not sufficient for executing the continuously generated computation-intensive or delay-sensitive tasks. We consider migrating computation tasks to other MEC servers to reduce the computation and communication pressure on current MEC server. In this article, we construct an MEC-based computation offloading framework for vehicular networks, which considers time-varying channel states and stochastically arriving computation tasks. To minimize the total cost of the proposed MEC framework, which consists of the delay cost, energy computation cost, and bandwidth cost, we propose a deep reinforcement learning-based computation migration and resource allocation (RLCMRA) scheme that requires no prior knowledge. The RLCMRA algorithm can obtain the optimal offloading and migration policy by adaptive learning to maximize the average cumulative reward (minimize the total cost). Extensive numerical results show that the proposed RLCMRA algorithm can adaptively learn the optimal policy and outperform four other baseline algorithms.