Abstract: A fast and accurate multigroup neutron diffusion calculation method was established for reactor core, and the semi-analytic nodal method (SANM) based on transverse-integrated diffusion equation was introduced within the framework of the analytic coarse mesh finite difference (ACMFD) formulation. Additionally, the ACMFD coupling coefficients were determined analytically from the SANM. In the SANM, the Legendre polynomials were employed to approximate the fission and scattering sources so that the analytic solution of transverse-integrated diffusion equation can be obtained. Furthermore, the 0th, 2nd and 4th-order Legendre polynomial representations were used respectively in order to perform fine-mesh and coarse-mesh calculations. The mumerical results show that the method possesses high accuracy and efficiency.