The governing equation of Peierls-Nabarro (PN) model is very complex, and its solution is given often without any solving process, which restricts the application of the PN model. A new method is proposed to describe the propagation of a mixed dislocation in a simple cubic crystal. First, the shear stress field and the dislocation density field on the slip plane are expressed as the trigonometric series and the first Chebyshev polynomial series, respectively, and then a set of governing equations are obtained; finally, the Newton-Raphson method is used to solve the governing equations. The results show that the method proposed in this paper is simple and effective for analyzing the propagation of mixed dislocations in a simple cubic crystal.