Firstly, by introducing modal coordinate transformation and matrix function transformation, the original damped system is transformed into a non-damped system. Secondly, by analyzing the properties of mode parameters with respect to non-damped system, the Frequency Response Matrix is worked out. Furthermore, by using inverse matrix transformation and inverse mode coordinate transformation, the precise response of originally damped system is derived. When the presented algorithm is applied to the classically damped system, the analytic equivalence to mode superposition method is obtained. And then the analytic expression involving non-classically damped system which can’t be done with by mode superposition method is obtained as well. Finally, the correctness and effectiveness of the methods given here are demonstrated by considering two examples respectively.