To address the problems that rule-based motion planning algorithms under constraints need pre-definition of rules and temporal features are not considered in deep learning-based methods, a motion planning model based on deep cascading neural networks was proposed. In this model, the two classical deep learning models, Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) network, were combined to build a novel cascaded neural network, the spatial and temporal features of the input images were extracted respectively, and the nonlinear relationship between the input sequential images and the output motion parameters were fit to achieve the end-to-end planning from the input sequential images to the output motion parameters. In experiments, the data of simulated environment were used for training and testing. Results show that the Root Mean Squared Error (RMSE) of the proposed model in four scenes including country road, freeway, tunnel and mountain road is less than 0.017, and the stability of the prediction results of the proposed model is better than that of the algorithm without using cascading neural network by an order of magnitude. Experimental results show that the proposed model can effectively learn human driving behaviors, eliminate the effect of cumulative errors and adapt to different scenes of a variety of road conditions with good robustness.