Abstract: Based on the complex modal theory and power series expansion theorem, a modal acceleration method for calculating the frequency response fonction (FRF) of viscous damped systems was derived. Compared to the typical modal superposition method, the proposed algorithm can reduce the modal trUncated errors significantly when modal mincation is adopted. The middle-high, low-high modal of the system can be truncated and accelerated according to the excited frequencies by using this method. Numerical example demonstrates that the present method is very efficient and the FRF has very high accuracy when only several items of the power series are considered.