Driving intention prediction from a bird’s-eye view has always been an active research area. However, existing research, on one hand, has only focused on predicting lane change intention in highway scenarios and, on the other hand, has not modeled the influence and spatiotemporal relationship of surrounding vehicles. This study extends the application scenarios to urban road scenarios. A spatial-temporal convolutional long short-term memory (ConvLSTM) model is proposed to predict the vehicle’s lateral and longitudinal driving intentions simultaneously. This network includes two modules: the first module mines the information of the target vehicle using the long short-term memory (LSTM) network and the second module uses ConvLSTM to capture the spatial interactions and temporal evolution of surrounding vehicles simultaneously when modeling the influence of surrounding vehicles. The model is trained and verified on a real road dataset, and the results show that the spatial-temporal ConvLSTM model is superior to the traditional LSTM in terms of accuracy, precision, and recall, which helps improve the prediction accuracy at different time horizons.