Considering that impact motion is not only a function of time but also dependent on phase-angle, we suppose the non-linear response of the vibro-impact system with time-varying mass is a function dependent not only on different time scale but also on the phase parameter. An approximate analytical solution of second order for the vibration is obtained by using Multi-Scales Method. The feasibility is verified by the numerical solution using Runge-Kutta algorithms. It is shown that the motion of the variable mass system has periodic behavior with the period of the changing mass, and the mass variation can only influence the system amplitude but not its cycle. However, the bigger the mass factor varies, the more intensive the response enlarges, and vice versa. The method and findings may be useful to analyze similar vibration systems with impact dampers or design the vibration control strategy.