The multi-terminal systems can be used as basic building blocks of nanoelectronic devices. However, the understanding of mode-dependent phonon transmission in these systems remains poorly developed. Hence, we examine the modal transmission processes for a T-shaped three-terminal structure, which has one zigzag graphene nanoribbon (GNR) vertically joined together with an armchair GNR as the side terminal. The atomistic Green’s function method is improved to be suitable for exploring the polarized phonon transmittance between terminals in the multi-terminal system, by treating the terminals in a uniform and standard way. Initially propagating along a zigzag GNR, the phonons turn 90° to the side terminal, or go straight ahead. The change of transport direction to the side terminal leads to a relatively low transmittance in most cases. However, the acoustic phonon transmittance spectrum has alternating prominent dips and sharp peaks, and can have a higher value even with the abrupt direction changing in some frequency ranges. Along the zigzag GNR, most of acoustic phonons do not change polarization mode after scattering. However, most of low frequency longitudinal (LA), transverse (TA), flexural (ZA) and rotational (ZA4) acoustic phonons convert into TA, LA, ZA4 and ZA phonons in the side terminal, respectively.