Abstract: The simplified spherical harmonics (SP_N) method is utilized to discrete the angular variables of Self-Adjoint Angular Flux (SAAF) neutron transport equation as spherical harmonics method has the disadvantage of large amount of calculation. To solve the unstructured geometry problem, the spatial variables of SAAF are discretized by using of finite element method. Numerical results of several test problems show that SP_N method can obtain high accuracy with a significantly higher computational speed than spherical harmonics (P_N) method, and can save more time when dealing with problems with higher dimension, larger amount of meshes, and larger expanding order N.