Vehicular ad hoc networks (VANETs) are regarded as essential ways for vehicles to share information with each other. As communication range is limited, multiple relay nodes are often required for establishing the multi-hop routing path between the source node and the destination node. Dependability of such routing path may be compromised due to different motion states of vehicles. In this paper, we address this challenge by designing a new next-hop selection scheme named LPLS (Long Path Lifetime Scheme), in which each relay node uses the optimal stopping theory to choose a suitable next-hop node. Especially, this selection scheme can balance the tradeoff between routing path lifetime and selection efficiency. The analysis and simulation results show that our next-hop selection scheme presents better performance with comparison to other reference schemes applied in the routing algorithms AODV and MOPR.