An attempt has been made to propose a flexure-based support of the high-precision base plates on Hard X-ray Imager (HXI), which is designed to investigate the non-thermal high-energy electrons accelerated in solar flares. This flexure support is designed to compensate thermal strain, which can lead to an unacceptable reduction of surface accuracy under rigid constraint. The flexure support proposed in this article is made up of eight separated single-side filleted flexure leaves, which are small and easy to manufacture. The flexure leaf's compliance matrix is derived from Castigliano's second theorem. Then the matrix is used, along with Finite Element Analysis (FEA), to determine the critical dimension of the flexure leaves. According to the result of finite element simulation, under a temperature change of +/- 5K, the in-plane torsion angle of the installation sites of grids are reduced to within 10 arcsec using flexure support. And the first-order natural frequency of the base plate with flexure support is 184 Hz, which is higher than the natural frequency and external disturbance frequency of general satellite carriers.