Due to the exposure of transmitted messages in public channels within Vehicular Ad-Hoc Network (VANET), many authentication schemes have been proposed to safeguard security and privacy. And in existing schemes, to expedite the authentication process for Vehicle-to-Infrastructure (V2I) communication, vehicles requesting authentication information from Certification Authority (CA) regarding the RSUs they are expected to encounter before the journey is recommended. However, the viability of the aforementioned schemes rely on two challenging prerequisites: complete trustworthiness of CA and the assurance that the Onboard Units (OBUs), which store secret keys permanently, remain impervious to physical attacks and cloning attempts. Hence in this paper, we propose a route privacy-preserving authentication scheme based on PUF in VANETs. Basing on Oblivious Transfer (OT) method, we let CA complete authentication keys distribution without knowing the route plan of a vehicle. We utilize Physically Unclonable Function (PUF) to minimize the exposure of private key. And as the output of a PUF is easily affected by objective factors, Fuzzy Extractor (FE) is used in our scheme to correct the challenge-response pair of it. In addition, the detailed security analysis proves that our scheme can meet the security requirements. Finally, the experimental analysis suggests that our scheme is lower than the other schemes in terms of time complexity.