Vehicle Ad Hoc Networks (VANET) and Internet of Vehicles (IoV) provide the effectiveness and convenience of people in traffic and transportation. They often make a large amount of information transmitted between vehicles and between vehicles and traffic management systems. They also increase the demand for vehicle computing and storage. In order to solve this problem, Vehicle Cloud Computing (VCC) uses a VANET combined with cloud computing technology to assist vehicle drivers for controlling vehicle-related data. Recently, Lee et al. revealed limitations and security problems in previous related studies and developed a more secure and efficient authenticated key agreement protocol for VCC to solve these limitations and problems. Although their study shows a formal security proof of their protocol and resistance to possible attacks, adopting a constant encryption key makes their scheme vulnerable to some possible attacks. This study states the security weaknesses of Lee et al.'s protocol, and develops an enhanced authenticated key agreement protocol for VCC. Compared with related works, the enhanced protocol overcomes the previous weaknesses, provides more security requirements, and retains a lower computational cost.