The atomistic Green’s function method is improved to compute the polarization resolved phonon transport in a multi-terminal system.Based on the recent developments in literature,the algorithm is simplified.The complex phonon band structure of a semi-infinite periodic terminal is obtained by the generalized eigenvalue equation.Then both the surface Green’s function and phonon group velocity in the terminal are determined from the wave modes propagating away from the scattering region along the terminal.With these key ingredients,the individual phonon mode transmittance between the terminals can be calculated.The feasibility and validity of the method are demonstrated by the chain example compared with the wave packet method,and an example of graphene nanojunction with three terminals.