The impedance value of the pedestal on a stiffened cylindrical hull directly reflects its resistance to the transmission of vibration waves. In this study, the topology optimization is used to obtain the pedestal with improved impedance and reduced weight. Taking a cuboid with the given dimensions as the research object, the mathematical model of topology optimization is established, in which the element densities is taken as the design variables. According to the optimization results, a new type of cantilever pedestal is obtained. On this basis, the position, size and shape of the main components of the new pedestal are further optimized. Then, the strength and vibration characteristics are calculated and compared. The final optimization results show that the optimized cantilever pedestal with three brackets and a closure plate can effectively improve the minimum impedance of the base. And the thickness of the middle bracket should be much larger than that of the two sides and the closure plate. Compared with the original scheme, the minimum impedance of the optimized pedestal increases by 8.67% while the weight of the structure decreases by 25.69%. The research work provides a good reference for the design of the pedestal.