This paper presents a new approach based on Feed-Forward multilayered Neural Networks (FNNs) for the transient and steady-state analysis of piecewise-linear circuits. Nonlinear circuits are changed by linear circuits containing switches together with some state matrices and control inequalities by using piecewise linearization approach. One of the two problems arising in the analysis of these circuits is that control inequalities belonging to piecewise linearized components and control times for internally or externally controlled components is needed to determine switching times. Another is that the analysis time is very long. The proposed approach is considered as the solution to the problems. FNNs are used for modeling the piecewise linear circuits. By using the obtained model networks, the switching sequence and switching times from one state to another for transient and steady states are determined. The transient and steady-state solutions are fast accomplished through this knowledge. As an example, a nonlinear circuit is used for demonstrating the utility of the proposed approach, and the results are compared with that of the model constructed at Matlab/Simulink. Example circuit is analyzed in the time of 1 h 42min by using the proposed approach but the time of 2 h 27 min by Matlab/Simulink. Moreover, simulation results demonstrate that the proposed approach yields more accurate approximation for the switched nonlinear circuits.