In recent years, with the development of intelligent vehicles and wireless sensor network technology, the research on road safety has attracted much attention in vehicular ad-hoc networks (VANETs). By sensing events on the road, vehicles can broadcast information to inform others of traffic jams or accidents. However, the mobile vehicle network has a large transmission delay, which makes real-time content transmission impossible. In this paper, a new certificateless aggregate signcryption scheme (CLASC) is proposed by using a fog computing framework that supports mobility, low latency, and location awareness. It is combined with online/offline encryption (OOE) technology, which reduces many time-consuming operations and improves the security of vehicle users and the efficiency of message authentication. In addition, the scheme has the characteristics of mutual authentication, anonymity, untraceability, and nondeniability. Based on the difficulty of the discrete logarithm problem (DLP) and the computational Diffie-Hellman (CDH) problem, the scheme is further proved to be unforgeability and confidentiality under the random oracle model. The simulation results show that compared with the existing schemes, this scheme can not only ensure the security requirements of the system but also achieve higher efficiency in computing and communication.