Vehicular Ad hoc networks (VANETs) as spontaneous wireless communication technology of vehicles has a wide range of applications like road safety, navigation and other electric car technologies, however its practicability is greatly hampered by cyber-attacks. Due to message broadcasting in an open environment during communication, VANETs are inherently vulnerable to security and privacy attacks. However to address the cyber-security issues with optimal computation overhead is a matter of current security research challenge. So this paper designs a secure and efficient certificate-less aggregate scheme (ECLAS) for VANETs applicable in a smart grid scenario. The proposed scheme is based on elliptic curve cryptography to provide conditional privacy-preservation by incorporating usage of time validated pseudo-identification for communicating vehicles besides sorting out the KGC (Key Generation Center) escrow problem. The proposed scheme is comparatively more efficient to relevant related research work because it precludes expensive computation operations likes bilinear pairings as shown by the performance evaluation. Similarly, communication cost is within the ideal range to most related works while considering the security requirements of VANETs system applicable in a smart grid environment.