Due to the characteristics of high-speed movement of vehicles, authentication between vehicles and roadside units (RSUs) needs to be performed quickly. Vehicles can obtain the authentication information of the relevant RSUs from the certification authority (CA) in advance through route planning. Fast authentication can be performed when the vehicle enters the RSU range. However, in most of the current vehicle-to-infrastructure (V2I) fast authentication schemes, when the vehicle requests the authentication information of an RSU from the CA, the vehicle often needs to provide the CA with the travel path information, which leads to the CA easily obtaining the travel path of the vehicle. In addition, the CA encrypts the private keys of RSUs and sends them to vehicles as authentication keys, and the vehicles can obtain the private key information of RSUs directly after decryption. Once the private keys of RSUs are leaked, vehicular ad hoc networks (VANETs) can be attacked by malicious access. In order to protect the confidentiality of RSU private keys and the route privacy of vehicles, we propose a privacy-preserving V2I fast authentication scheme in VANETs. The scheme realizes the confidentiality of RSU private keys and the route privacy protection of vehicles by improving the oblivious transfer (OT) algorithm. Security analysis proves that our scheme has good privacy and attack resistance. Finally, performance evaluation shows that the proposed scheme performs better in terms of computational overhead and communication overhead compared to related schemes.