The decomposition method is a nonnumerical method of solving strongly nonlinear differential equations. In this paper, the method is adapted for the solution of the one-dimensional nonlinear Poisson’s equations governing the linearly graded p-n junctions in semiconductor devices, and the error analysis for the approximate analytic solutions obtained by the decomposition method is carried out. The simulation results show that the solutions obtained by the method are accurate and reliable, and that the quantitative analysis of the linearly graded p-n junctions can be conducted. This work indicates that the decomposition method has some advantages, which opens up a new way for the numerical analysis of semiconductor devices.