The relation between electrical circuit and traffic network has been proposed by Sasaki and Inouye, but they proposed link cost function is a linear function which cannot present the congestion situation. Cho and Huang extended the link cost function to a nonlinear function which can explain the congested network. In this paper, we proposed a foremost and novel approach to solve the traffic assignment problem (TAP) by simulating the electrical circuit network which consists of nonlinear link cost function models. Comparing with the solutions of Frank-Wolfe algorithm, the simulation results are nearly identical. Thus, the simulation of a network circuit model can be applied to solve network traffic assignment problems. Finally, two examples are proposed, and the results confirmed that electrical circuit simulation is workable in solving congested network traffic assignment problems.