Dynamic traffic assignment (DTA) methods have been developed fruitfully in theory but are limited in application. Reasons may include the high computational complexity, the difficulty in model calibration, and the reliance on accurate and complete origin–destination (OD) data. Recognizing the incompleteness of OD data in the real world, this paper proposes a deep learning-based DTA model. Specifically, a convolution neural network (CNN) is chosen to account for the spatial correlation of OD pairs. The CNN-based DTA model is trained with the input of historical OD data (incomplete because of limited survey tools) and the output of link flow data (complete thanks to detection technologies). These data are obtained first by simulations in experimental networks and then from an empirical survey in Dazhou, China. Extensive experiments are done about various levels of data incompleteness (measured by the percentage of missing OD data). Comparisons show that the trained CNN-based DTA model performs better with higher accuracy than other common statistical/machine learning algorithms (e.g., feed-forward neural network, k-nearest neighbor, and Kriging). The proposed model also shows robustness to the small-sized dataset, data noise, and network changes. Additional examinations include employing the proposed framework to learn and estimate traffic flow characteristics (i.e., average speed and travel time) and the dynamic flow of turning movements at intersections. Lastly, a case study demonstrates the application of the proposed model using real data. Overall, this study indicates the promising prospect of the CNN-based DTA model as a supplement to traditional ones.