In order to suppress the effect of the temperature variation on the wavefront of the laser communication terminal, the secondary mirror support with flexure hinges is designed. The series-wound straight-circle flexure hinge is designed to achieve the maximal variation range of the flexibility or stiffness with the limit of flexure hinges’ geometrical size. The position and quantity of the flexure hinges are determined to control the deformation direction of the secondary mirror. In order to search the direction in which the wavefront aberration is minimum, the flexure hinges’ parameters are optimized with the system wavefront aberration as the optimization objective. The prototype of the laser communication terminal is constructed and the value of the wavefront aberration is measured under the condition of 20±2°C. Experimental results show that the value of the wavefront aberration root mean square (RMS) is reduced from 0.066λ to 0.042λ, meeting the requirement of RMS less than 1/20λ (λ=632.8 nm). The athermal design method presented in this paper provides a novel way for the athermal design of the small aperture mirror support in off-axis optical systems.