The heterogeneous vehicular network (HetVNET), which consists of multiple radio access networks (RANs), is a promising paradigm to provide a variety of services on the road. However, with the diverse quality of experience (QoE) requirements for vehicles, how to choose the optimal network for the vehicles pose great challenges. In this paper, we investigate the network selection problem in a HetVNET, which includes LTE-vehicle-to-anything (LTE-V2X), dedicated short-range communications (DSRC), WiFi. The network selection problem is formulated as a stable matching between the vehicles and different RANs. A two-sided one-to-many matching algorithm is presented based on the preference lists of both vehicles and RANs. Numerical simulation results show that the proposed method can improve the total throughput of the system and reduce the total network switch time compared to some existing algorithms.