With the aim to improve the effect of the primary support of a space High Resolution Imaging Spectrometer (HRIS) on its stability of optic-mechanic system, the requirements were analyzed for the rigidity and heat stability of a common space remote sensor. The traditional support structures to the space optical remote sensors were introduced.As the traditional supports by lags could not meet the need of the three-mirror anastigmatic (TMA) imaging system, a new coupling support structure by two axes was presented and its theory was analyzed.The finite element analysis of a 3D model was realized by software MSC.PATRAN during the optimum designing. The results show that the first order natural frequency is 95 Hz under sine vibration loading. The maximum RMS value and the maximum PV value of the mirror surface aberration are 12 nm and 60 nm under both of a 10 ℃ temperature fall and the influence of the gravity,respectively. The angle rotation by the Z axis of primary mirror is reduced from 55″ to 12″. The spectral data of the optical system under the hot vacuum environments verify the analysis results,which shows the coupling support structure is able to meet the needs of the rigidity and the heat-stability of optic-mechanic systems.