In the near future, vehicle-to-vehicle and vehicle-to-roadside infrastructure communications will enable numerous applications, such as collision avoidance, traffic management, location-based services, and infotainment for the automobile field. Position and velocity play important roles in these applications such as collision avoidance. Forged position or velocity information will make a severe impact on both performance and security of the vehicular ad-hoc network (VANET). The main challenges in developing secure position and velocity schemes for VANETs are the highly dynamic environment and cost constraints. In this paper, we propose a position and velocity verification scheme. Then via ns-2, we simulate the proposed scheme in various vehicular mobility environments including rural, urban and Manhattan. Finally, we evaluate the proposed scheme for both position and velocity verifications with automotive grade differential global positioning system (DGPS) and intentionally induced errors as well. The performance evaluation results show that (1) our scheme is very precise in both position and velocity verifications and (2) the proposed scheme is very robust in position verification for rural, urban and Manhattan scenarios even if the introduced errors are in the order of 10 m. Copyright © 2010 John Wiley & Sons, Ltd.