Cognitive radio technology can effectively improve spectrum efficiency in wireless networks and is also applicable to vehicle small-cell networks. In this paper, we consider the problem of spectrum sharing among a vehicle primary user (V-PU) and multiple vehicle secondary users (V-SUs). This problem is modeled as a competition market, and the solution for V-SUs is designed using a non-cooperative game. A utility function that measures the profit of the V-PU considering quality of service (QoS) is proposed, aiming at maximizing the profit of the V-PU. Nash equilibrium is obtained as the best solution in our game. Then, the realistic vehicle-enabled cognitive small-cell network is considered in building the dynamic spectrum allocation problem. The V-SUs adjust their current strategies gradually and iteratively based on the observations on the strategies of the previous moment. This adjustment parameter is controlled by the frequency of adjustment. The stability analysis of the dynamic game is given out subsequently for dynamic spectrum allocation. The numerical results show the effectiveness of the proposed dynamic spectrum scheme for vehicle-enabled cognitive small-cell networks and Nash equilibrium point’s existence.