Vehicle platooning poses a viable solution to the increasing traffic congestion seen around the world. It relies on wireless communication channels for the vehicles in a platoon to interact with base stations and other vehicles in the network. However, due to the open nature of these channels, there exists a potential risk to the platoon's security. Moreover, since platoon vehicles move at sufficiently fast speeds, the responsiveness and efficiency of the network governing the platoon cannot be overlooked. In this paper, we propose an efficient yet secure platoon management scheme that can resist cyber-attacks such as replay, man-in-the-middle, and Sybil attacks during major platoon events. BCVerifier is used to evaluate the security functionality of the blockchains deployed with the proposed scheme. Finally, the performance of the proposed scheme is evaluated to show its efficiency in terms of computational and communication costs.