The novel support structure design of high stability for space borne primary mirror is presented. The structure is supported by a ball head support rod, for statically determinate support of reflector. The ball head assembly includes the supporting rod, nesting, bushing and other important parts. The liner bushing of the resistant material is used to fit for ball head approximated with the reflector material, and then the bad impact of thermal mismatch could be minimized to minimum. In order to ensure that the structure of the support will not be damaged, the glue spots for limitation is added around the reflector, for position stability of reflector. Through analysis and calculation, it can be seen that the novel support structure would not transfer the external stresses to the reflector, and the external stresses usually result from thermal mismatch and assembly misalignment. The novel method is useful for solving the problem of the bad influence form thermal stress and assembly force. In this paper, the supporting structure is introduced and analyzed in detail. The simulation results show that the ball head support reflector works more stably.