As a critical technology of network security, key management has attracted attention in mobile edge computing (MEC)-enabled vehicular networks. However, the traditional centralized key management methods are vulnerable to single points of failure. In this case, we propose a distributed key management scheme for MEC-enabled vehicular networks. Within this scheme, we use permissioned blockchain to store the key and present a new transaction format while key registration, update, and revocation are included. Considering the high mobility of the vehicle, we design a lightweight mutual authentication protocol to ensure that the vehicle can access MEC servers quickly and safely. Finally, the simulation results prove that our proposed scheme can achieve a lower authentication delay, less communication overhead, and higher security compared with traditional key management.