In this article, we propose a secure and effective blockchain-enabled privacy-preserving authentication scheme for the transportation cyber-physical system (CPS) with the cloud-edge computing environment, which supports unconditional anonymity and data batch integrity verification while greatly simplifying key management issues. The proposed privacy-preserving authentication scheme employs an elliptic curve to construct a pairing-free ring signature scheme, which greatly reduces the resources overhead in the transportation CPS with cloud-edge computing. Moreover, the authentication process is performed on the blockchain to provide more reliable service information for vehicular communication. Furthermore, the security proof of the scheme is demonstrated based on the elliptic curve discrete logarithm problem under the random oracle model, and gives the corresponding security analysis. Finally, a simulation experiment demonstrates that the proposed scheme is feasible compared with the existing schemes.