The Vehicular Ad hoc NETworks (VANETs) are of high mobile and dynamic in nature. They are highly prone to network discontinuity, thereby the applications running on the vehicles get degraded in its service. The network selection for VANETs is done based on network attributes and user Quality of Service (QoS) demands. In this work, a two-phase access network selection scheme is proposed for VANETs. In the first phase, the available networks are ranked based on QoS demands using Weighted Sum Method (WSM). During the second phase, based on availability of resources, handoff decision and access network selection are carried out using game theory approach. Here, the vehicle and network play the game by adopting different strategies, thereby the optimum Nash Equilibrium (NE) is obtained. The simulation results validate that the proposed scheme outperforms the conventional Multiple Attribute Decision Making (MADM) schemes. © 2021 World Scientific Publishing Company.