Studies on self-driving transport vehicles have focused on longitudinal and lateral driving strategies in automated structured road scenarios. In this study, a double parallel network (DP-Net) combined with longitudinal and lateral strategy networks is constructed for self-driving transport vehicles in structured road scenarios, which is based on a convolutional neural network (CNN) and a long short-term memory network (LSTM). First, in feature extraction and perception, a preprocessing module is introduced that can ensure the effective extraction of visual information under complex illumination. Then, a parallel CNN sub-network is designed that is based on multifeature fusion to ensure better autonomous driving strategies. Meanwhile, a parallel LSTM sub-network is designed, which uses vehicle kinematic features as physical constraints to improve the prediction accuracy for steering angle and speed. The Udacity Challenge II dataset is used as the training set with the proposed DP-Net input requirements. Finally, for the proposed DP-Net, the root mean square error (RMSE) is used as the loss function, the mean absolute error (MAE) is used as the metric, and Adam is used as the optimization method. Compared with competing models such as PilotNet, CgNet, and E2E multimodal multitask network, the proposed DP-Net is more robust in handling complex illumination. The RMSE and MAE values for predicting the steering angle of the E2E multimodal multitask network are 0.0584 and 0.0163 rad, respectively; for the proposed DP-Net, those values are 0.0107 and 0.0054 rad, i.e., 81.7% and 66.9% lower, respectively. In addition, the proposed DP-Net also has higher accuracy in speed prediction. Upon testing the collected SYSU Campus dataset, good predictions are also obtained. These results should provide significant guidance for using a DP-Net to deploy multi-axle transport vehicles.