Abstract: TMT(Thirty Meter Telescope) was a Ritchey Chrtien optical-infrared thirty meter telescope with 3.594 m2.568 m ellipse flat one and 1 800 kg weight. The tertiary mirror system reflected the light coming from the secondary mirror(M2S) to the science instruments which mounted on the telescope Nasmyth platforms. It had tracking and slewing functions. Tertiary mirror support system included axial support system and lateral support system. Based on the mirror surface figure error requirements, the paper proposed axial support system used 18 point whiffletree structure with surface figure RMS of 118.5 nm after optimum. The surface figure RMS can reach 4.7 nm by the lateral support, and the surface figure RMS was less than 77 nm by axial and lateral support. Based on this support program, the mirror support structure is designed to satisfy weighted and volume requirements.