Named Data Networking replacing the TCP/IP architecture has emerged as a state-of-the-art tendency in VANETs because of its high efficiency in content distribution and Vehicle-to-Vehicle (V2V) communications. After this paradigm shift in VANETs, the traditional gateway selection algorithms and Peer-to-Peer content downloading protocols become inappropriate for vehicles to cooperatively acquire big-size Internet contents from roadside infrastructures (e.g. LTE-BS). To address this problem, we propose a Prior-Response-Incentive-Mechanism (PRIM) to stimulate vehicles to take part in cooperative downloading in VANETs-LTE heterogeneous network and we use game theory to analyze vehicles behaviors and find the optimal strategy for each cooperator. In consideration of the effect of mobility, wireless channel and Named Data in VANETs, the mechanism can fulfill vehicles demand timely and properly evaluate vehicles contributions. Simulation results based on ndnSIM show that the proposed mechanism can dramatically reduce repeated downloading, promote cooperation among vehicles with less delay and overhead, under the premise of obtaining integrated target content.