 This paper presents a new approach for optimizing the parameters of tuned mass dampers, TMDs, which are commonly used in civil engineering, aerospace, machinery, and other fields. The authors derive an approximate analytical solution of TMD amplitude using the complex variable averaging method, CDAM. They then compare the computational time consumption of this method with the numerical method, NM. The results show that the optimized parameters of the TMD obtained by CDAM possess a better vibration reduction effect both before and after the TMD generates nonlinear characteristics. Furthermore, the CDAM generated frequency response times faster than the NM.