In the traditional vehicular network, computing tasks generated by the vehicles are usually uploaded to the cloud for processing. However, since task offloading toward the cloud will cause a large delay, vehicular edge computing (VEC) is introduced to avoid such a problem and improve the whole system performance, where a roadside unit (RSU) with certain computing capability is used to process the data of vehicles as an edge entity. Owing to the privacy and security issues, vehicles are reluctant to upload local data directly to the RSU, and thus federated learning (FL) becomes a promising technology for some machine learning tasks in VEC, where vehicles only need to upload the local model hyperparameters instead of transferring their local data to the nearby RSU. Furthermore, as vehicles have different local training time due to various sizes of local data and their different computing capabilities, asynchronous federated learning (AFL) is employed to facilitate the RSU to update the global model immediately after receiving a local model to reduce the aggregation delay. However, in AFL of VEC, different vehicles may have different impact on the global model updating because of their various local training delay, transmission delay and local data sizes. Also, if there are bad nodes among the vehicles, it will affect the global aggregation quality at the RSU. To solve the above problem, we shall propose a deep reinforcement learning (DRL) based vehicle selection scheme to improve the accuracy of the global model in AFL of vehicular network. In the scheme, we present the model including the state, action and reward in the DRL based to the specific problem. Simulation results demonstrate our scheme can effectively remove the bad nodes and improve the aggregation accuracy of the global model.