For the problem of multi-attribute group decision-making with heterogeneous preference information on attribute values and overall preference orderings on alternatives, this article proposes a neural network-based approach. In the approach, firstly, the heterogeneous preference information on attribute values and overall preference orderings on alternatives are normalized. Secondly, based on the normalization results, two optimization models are set up to determine attribute weights and expert weights, respectively. Thirdly, two neural networks are set up and trained to determine attribute weights and expert weights based on the optimization models. Then, the overall values of the alternatives are obtained as well as their rankings. Simulations on the proposed neural networks are conducted for illustrations.