Aiming at the problem that temporal-spatial features affect the trajectory prediction accuracy of autonomous vehicle, a temporal-spatial multi-head attention (TSMHA) vehicle trajectory prediction model was proposed. For the feature information of spatial and temporal dimensions, the multi-head attention mechanism was used to extract the spatial interaction perception and temporal motion pattern of the vehicle. The processed temporal-spatial feature information was transmitted to the gate fusion model for feature fusion, in order to obtain complementary features and remove redundancy. Using the encoder-decoder structure based on long short-term memory (LSTM), future trajectories were recurrently generated considering the potential interaction between trajectories during encoding and decoding. In the training process, the L2 loss function was used to reduce the difference between the predicted trajectory and the ground-truth trajectory. Experimental results show that, compared with the comparison models, the accuracy of the proposed model was improved by 3.95% in the highway, 15.64% in the urban roads, and 31.40% in the roundabout scenario.