Abstract: The spherical harmonics method for neutron transport equation on unstructured-meshes is derived based on a new second order neutron transport equation, self-adjoint angular flux （SAAF） equation. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variables, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation code is programmed according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision result and avoid the ray effect very well.