In order to meet the requirements of high strengthen, stiffness and thermal dimensional stability for large aperture space mirrors, materials selection, lightweight pattern and the design of the support were taken into account in the design of some large aperture space mirror which is the most important optical components in a three mirror off-axis space telescope. SiC was chosen as the material of mirror and a new design with back semi-closed circular reinforced ribs lightweight structure was proposed. Mirror with the back three-point support scheme, through the rational design of flexible support structure parameters to ensure high stiffness and thermal environment adaptability. By adopting finite element analysis technique, the mirror component was analyzed detailed. Analysis results indicate that the surface figure accuracy can reaches to PV <= lambda/10, RMS <= lambda/40(lambda = 632.8nm) under gravity and 2 degrees C uniform temperature rise, and the first order natural frequency is 151Hz, the static, dynamic stiffness and thermal dimensional stability is high enough, which can meet the design requirements.