Blockchain technology has considerable potential to enhance vehicle platoon management by providing robust security guarantees. Nevertheless, existing blockchain-based platoon management schemes suffer from inefficiency and poor scalability, imposing excessive computation and communication overheads on the resource-constrained vehicle side. To overcome these limitations, in this paper, we propose a Blockchain-based scheme for secure and efficient Vehicle Platoon Management (BVPM). Specifically, we introduce an enhanced Practical Byzantine Fault Tolerance algorithm with Collective Signing (CS-PBFT), which leverages a communication tree structure and Schnorr multisignatures to improve blockchain performance. In addition, we propose a distributed voting algorithm for leader election based on the Subpath Signature and Raft (SS-Raft) mechanism, where a novel subpath signature quantifies path similarity among vehicles. Security analysis demonstrates that the BVPM scheme provides robust security for platoon operations against several common attacks. Extensive simulations further reveal that, compared with the existing schemes, the BVPM scheme significantly reduces computation and communication overheads.