Thirty Meter Telescope (TMT) is a 30 m Ritchey-Chrétien optical-infrared telescope. It tertiary mirror (TMT M3) is an elliptical flat mirror with the aperture of 3.594 m×2.568 m and weight of 1.8 t. The M3 system reflects the light coming from the secondary mirror system (M2S) to the science instruments that are located on the Nasmyth platforms, and the M3 System must rotate and tilt as the telescope tilts about the elevation axis and tracks astronomical objects across the sky. The M3 support system should support the M3 mirror so that the mirror surface figure will be less than λ/5 (wavelength λ=632.5 nm) or root-mean-square (RMS) slope will be less than 1 μrad. The M3 support system includes axial support system and lateral support system. The axial support system uses 18-point whiffletree structure, and after optimization the RMS mirror surface figure achieves 118.5 nm. When the tertiary mirror surface figure error cannot meet the requirement with the support structure, correct moment is used to corrective the surface figure error.