A new bud-shaped moth-eye structure (BSMS) with a parabolic center section was designed based on the excellent anti-reflection performance of the traditional parabola-shaped moth-eye structure (PSMS). With the finite-difference time-domain (FDTD) method, we determine the best bottom diameter to be 200 nm by comparing the average reflectance of PSMSs with different bottom diameters and heights. On this basis, the reflectance and cross-sectional electric field intensity distribution of PSMS, BSMS, and a cone-shaped moth-eye structure (CSMS) at different heights were analyzed. Furthermore, the anti-reflection performance of BSMS was assessed with the equivalent medium theory. The results show that the average reflectance of BSMS is lower than that of both PSMS and CSMS in the wavelength range of 300--1200 nm and the height range of 300--1000 nm; when the bottom diameter is 200 nm and the height is 800 nm, the average reflectance of BSMS is as low as 0.19%, and its anti-reflection effect is about 3.5 times that of PSMS and 3.8 times that of CSMS. BSMS demonstrating excellent and stable anti-reflection performance provides a reference for the further design and optimization of anti-reflection structures.