To meet the requirement for high stiffness and lightweight, topology optimization method with constraints of static displacements and first resonance frequency was studied in 4 m telescope mount base design. Firstly, mathematical model of topology optimization was built subjected to minimum compliance, with pseudo density of the finite elements as design variables, static displacements, first resonance frequency and total mass as optimization constraints. Procedure of calculating sensitivities of optimization objective was presented in detail. Furthermore, topology optimization method was applied in mount base design, based on which shape and size design were carried out. Finally, the static stiffness and dynamic behavior of the optimized structure was analyzed and checked using the finite element method. The achieved results show that total mass of mount base reduces from 27.66 t to 22.15 t, while the maximum displacement decreases from 0.037 7 mm to 0.014 mm and first resonance frequency increases from 217.1 Hz to 247.45 Hz, ie, improving static and dynamic performances with lots of mass cut, which validate the presented topology optimization method. This topology optimization method will provide efficient help to other components′ design of 4m telescope mount.