Internet of Vehicles (IoV) plays an important role in enhancing the intelligence of social transportation services. However, there are existing such as privacy leakage, computational complexity and low efficiency on V2R authentication protocols. To solve these problems, a lightweight V2R authentication protocol according to physical unclonable function (PUF) and Chebyshev chaotic map is proposed. The lightweight property of PUF in this scheme can solve the resource constraint problem of the On-Board Unit (OBU) effectively. The fuzzy extractor can correct for small variations in PUF response and improve the accuracy of data transmission. Besides, Chebyshev chaotic map with good cryptographic properties establishes a secure session key while achieving mutual authentication of V2R. Finally, simulation results show that the scheme combining PUF, chaotic map, and fuzzy extractor in this paper saves 4.7% to 49% in communication and calculation overhead comparing with existing protocols. In terms of security, our scheme can also meet the requirements well in the V2R authentication protocol for IoV.