Abstract: The SP₃ equation is an approximation of the 3^rd-order spherical harmonic method.Relative to the diffusion theory,it has higher accuracy for calculation.Adopting the nonlinear iterative method to solve the SP₃ equation,and putting forward the coupling relationship with Angular discrete,the problems of the complexity about the coupling relationship in the vacuum-boundary and the numerical instability during correction for 2^nd-order flux are successfully solved.A code named NLSP₃ for solving the SP3 equation with nonlinear iterative method was developed.Through the calculation of the benchmark problems,the feasibility of the algorithm is proved.