Based on Venigalla's work, we mainly constructed a multiclass, multimode nonadditive path costs traffic assignment model with emission effects under different engine operating modes. Then, we used a path-based gradient projection (GP) algorithm to solve the mathematic model we put forward. After that, we applied the model as well as the GP algorithm into Charlotte network as a numerical example. In particular, we considered different network structures and different locations in the model so that it can simulate on-road vehicle situation. Compared with the F-W algorithm, it can be shown that GP algorithm has a rapid convergence speed than FW algorithm. The results also demonstrate that GP algorithm could be widely used in solving the traffic assignment problem with nonadditive path costs.