Stable and efficient routing plays a key role for the success of VANETs. Road-based routing has been shown well-suited for urban VANETs, and multipath routing provides alternative routes once the current route fails. However, existing multipath routing protocols are node-based, which are not suitable for urban VANETs. In this paper, we propose a road-based QoS-aware multipath routing protocol for urban VANETs (RMRV). The proposed RMRV can find multiple paths and intelligently utilize them. We also propose a space-time planar graph approach to predict the connectivity of each road section (RS) in a path, and then derive the path's future lifetime and life periods. In this way, the source node may dynamically switch to use a path with the longest lifetime. The life periods of a path can further be utilized to estimate the packet delay for QoS routing. Simulation results show that comparing to RBVT-R, which is a single-path road-based routing protocol, the packet delivery ratio of the proposed RMRV (only one path used at a time) is 12.2% higher than that of RBVT-R, and the average end-to-end delay of RMRV is 11.5% lower than that of RBVT-R, on average. To the best of our knowledge, there is no existing road-based multipath routing protocol for VANETs.