A beam orbit stability of 0.1 μm is required by the High Energy Photon Source (HEPS). As an important system of the storage ring, the beam position monitors (BPMs), together with the measured data, play an important role in the beam orbit monitoring and stabilization. Resolution of 0.1μm and long-term stability is required for the BPMs. In order to suppress the mechanical deformation caused by mechanical vibration and temperature variation, an independent and stable support system for the BPM-pick-ups is indispensable to have a higher eigen-frequency in lateral, a smaller vibration amplification ratio, and a minimum temperature deformation factor. In this paper, Invar36 alloy is selected as the main material of the support structure since it has good temperature stability. To ease manufacture and installation, the rod and plate structure is selected for the support prototype, and thorough simulation is done to find the optimal structure. With the methods of topology optimization in ANSYS, the structure prototype of the maximum eigen-frequency is found to guide the design of the support. The support is tested in the laboratory. Comparison between the measurements and the simulation results is made for installation improvement. Four methods of installation is tested and the results will provide reference for the support installation in the storage in the future.