The Origin-Destination (OD) data collection often relies on the questionnaire surveys which is inevitably incomplete. With incomplete input data, the traditional traffic assignment models (e.g., mathematical programming) cannot generate reasonable results. Alternatively, we propose a deep-learning approach employing Feed-Forward Neural Network (FFNN) for the traffic assignment that respects incomplete data. Experiments are conducted in the Braess's paradox network, Sioux Falls network, and Chicago sketch network. In the first two networks, training data for the FFNN is obtained by randomly generating 10000 OD scenarios and running mathematical assignment models for link flows. For Chicago sketch network, a mesoscopic tool is employed to generate the training data. The feasibility of using FFNN to learn traffic assignment mechanics is verified by using complete OD data and full link flow data with accuracy over 90% in three networks. In case of partially observed OD data, our idea is to learn the mapping between incomplete OD data and full link flow data. Experiments are conducted under different OD data incompleteness levels. The results demonstrate that the accuracy of FFNN model remains over 90% even losing 50% OD data and overwhelms that of the mathematical assignment model in three networks. Practically, the reported model can be trained for a certain network with easily-obtained partial OD data (e.g., observed cellular mobile data) and traffic flow data in the field (e.g., loop data and video data). Once well trained, when inputting voluminous incomplete OD data, the data-driven approach can provide accurate full link flows efficiently.