Existing conditional privacy-preserving authentication schemes utilized in Vehicular Ad-hoc Networks (VANETs) to satisfy security and privacy requirements essentially depend on point multiplication operations. Achieving repaid verification method of the message is commonly suffer performance efficiency from resulting overheads. We propose a conditional privacy-preserving authentication scheme to secure communication and perform better performance efficiency in this article. The proposed scheme only depends on an elliptic curve cryptography (ECC) based on a point addition operation instead of a point multiplication operation during signing and verifying messages. In the joining phase of the proposed scheme, the vehicle requires the joining process for the broadcasting traffic-related message to others or nearby RSU within its communication range. After obtaining the pseudonym and secret key from RSU, the vehicle is considered as a registered node in VANET. This article utilizes a Burrows-Abadi-Needham (BAN) logic to evidence that the proposed scheme fulfill successfully mutual authentication. The formal security phase shows that security and privacy requirements are satisfied by the proposed scheme. The performance efficiency shows that our proposed scheme has lower overhead in terms of computation cost compared with other recent schemes since a point multiplication operations based o ECC are not used. Therefore, the computation costs of the message signing, individual-authentication and batch-authentication in our proposed scheme are decreased by 99.3%, 99.7% and 98.1%, respectively.