This research suggests the efficient numerical scheme to analyze the time-response of steady-state vibration of modal beam model when the properties (stiffness, damping) of the model are time-varying. The piping system conveying harmonically pulsating fluid is a typical example of parametrically excited system because the properties such as stiffness and damping are time-dependent characteristics. To analyze the time-response of this system, numerical integration method of differential equations, such as the Runge-Kutta method was usually used. But this method requires extensive computational efforts to solve the time-response of time-varying systems. In this paper, the governing equation was transformed to a single degree-of-freedom model at a certain mode by using assumed-mode method. A new method to predict efficiently the steady-state response for a time-varying system was presented. The steady-state response was assumed to have the frequency of the pulsation and its multiples, and was predicted by comparing the coefficients of Taylor series expansion. The efficiency of this method was validated by the comparison with conventional numerical method of differential equations and experimental results.