Compared to 3rd-generation light sources, 4th-generation SR light sources improve the brightness by reducing the emittance of the electron beam. To ensure the extremely low emittance of electron beams, it is necessary to provide more accurate beam position measurement. In this paper, we present a design of Button Beam position monitor (BPM) for a diffraction-limited storage ring in the low-energy region of the 4th-generation light source. The main work is focused on optimizing the physical design and mechanical structure of BPM feedthroughs, by minimizing the wakefield caused by electron beam and maximizing the voltage signals picked up by the electrodes. The design results improve the BPM position measurement resolution to meet the target of measurement requirements. This work is fundamental for the subsequent development of BPM electronics and fast orbit feedback system.