Position service is essential for positionbased ad-hoc routing, which is one popular routing mechanism for Vehicle ad-hoc networks (VANETs). In this paper, a controllable privacy protection scheme for position service in VANETs is proposed and evaluated. Our scheme integrates a vehicle authentication mechanism, and a Random activation proxy (RAP) mechanism with the common VHR-based position service. The authentication mechanism can achieve a conditional anonymity to the vehicles by using the group signature, and guarantee the security of the position service. RAP can defend the local tracking privacy attacks in the VANET where the identifiable areas are widespread. Privacy protection analysis indicates that our scheme achieves location privacy protection to the participant vehicles at a reasonable cost. Evaluation results show that the random silent period in our scheme can improve and configure the anonymity of the participant vehicles.