Internet of Vehicles (IoV) is an intelligent application of IoT in smart transportation, which can make intelligent decisions for passengers. It has drawn extensive attention to improve traffic safety and efficiency and create a more comfortable driving and riding environment. Vehicular cloud computing is a variant of mobile cloud computing, which can process local information quickly. The cooperation of the Internet and vehicular cloud can make the communication more efficient in IoV. In this paper, we mainly focus on the secure communication between vehicles and roadside units. We first propose a new certificateless short signature scheme (CLSS) and prove the unforgeability of it in random oracle model. Then, by combining CLSS and a regional management strategy we design an efficient anonymous mutual quick authentication scheme for IoV. Additionally, the quantitative performance analysis shows that the proposed scheme achieves higher efficiency in terms of interaction between vehicles and roadside units compared with other existing schemes.