With the advancements in social media and rising demand for real traffic information, the data shared in vehicular ad hoc networks (VANETs) indicate that the size and amount of requested data will continue increasing. Vehicles in the same area often have similar data downloading requests. If we ignore the common requests, the resource allocation efficiency of the VANET system will be quite low. This project proposes a efficient and privacy preserving data downloading scheme for VANETs, based on the edge computing concept. In the proposed scheme, a roadside unit (RSU) can find the popular data by analyzing the encrypted requests sent from nearby vehicles without having to sacrifice the privacy of their download requests. Further, the RSU caches the popular data in nearby qualified vehicles called edge computing vehicles (ECVs). If a vehicle wishes to download the popular data, it can download it directly from the nearby ECVs. This method increases the downloading efficiency of the system. The security analysis results show that the proposed scheme can resist multiple security attacks. The performance analysis results demonstrate that our scheme has reasonable computation and communication overhead. Finally, the OMNeT++ simulation results indicate that our scheme has good network performance.