The paper mainly proposed a novel kinematic triad-pod flexure mount for supporting a primary mirror in space. This kind of mount is constructed by three identical pods, each of them is consisted of four rotation flexures with virtual rotation center. The mount can realize great releasement of thermal stress effect on primary mirror caused by CTE (Coefficient of Thermal Expansion) mismatch between baseplate and mirror at cryogenic temperature. Based on principles of kinematic design, the paper firstly proposes a mount configuration with three pods arranged with inclined angle. Then, the structure of pod is designed in detail, and compliance model is established. A study case is employed to illustrate how to design a triad-pod mount with higher supporting stiffness and large radialcompensate compliance. Finally, simulations by FEM are implemented to verify and analyze the performances of the proposed mount. The results demonstrate that the mount can further reduce the thermal stress in primary mirror while maintaining nearly indistinctive supporting stiffness than traditional three-bipod mount. Hence, the proposed mount can provide foundation to achieve a mount with greater performances for supporting a large-aperture mirror at a wider range of temperature.