In this paper, we present a QoS routing protocol called GVGrid for multi-hop mobile ad hoc networks constructed by vehicles, i.e., vehicular ad hoc networks (VANETs). GVGrid constructs a route on demand from a source (a fixed node or a base station) to vehicles that reside in or drive through a specified geographic region. The goal of GVGrid is to maintain a high quality route, i.e. a robust route for the vehicles movement. Such a route can be used for high quality communication and data transmission between roadsides and vehicles, or between vehicles. The experimental results have shown that GVGrid could provide routes with longer lifetime, compared with an existing routing protocol for VANETs