Until now, some protocols have been presented to provide vehicle's anonymity and unlinkability in VANET by means of issuing multiple anonymous certificates to each vehicle from the trust authority, or shot-time anonymous certificate to a vehicle after mutual authentication between a Roadside Unit (RSU) and the vehicle. However, these protocols have high overheads of the trust authority, RSUs and vehicles for generating anonymous certificate. In this paper, we propose an efficient anonymous authentication protocol, in which RSUs can issue multiple shot-time anonymous certificates to a vehicle to alleviate system overheads for mutual authentication between vehicles and RSUs. Several simulations are conducted to verify the efficiency of the proposed protocol in terms of RSU valid serve ratio and vehicle's computational costs. Moreover, the proposed protocol provides unlinkability and traceability when multiple RSUs are compromised, whereas previous protocols do not provide unlinkability and traceability.