Resolving traffic assignment problems with a logit model will result in some error because of the correlation of the trip cost and the flux, whereas the application of the random equilibrium assignment model is confined for its complex arithmetic. An amelioration of the logit model and a step by step arithmetic are implemented. The improved model is simple, rational and easily resoluted and the relationship of the trip cost and flux is also considered, therefore, it is applicable for the congested assignment problem and possesses widely applying prosperity.