Analysis of balancing balls of auto-balancer for reducing non-synchronous motion in passing critical speed is performed. Equations of motion of the auto-balancer mechanism including balancing balls are modeled based on non-stationary vibration model. Time-variant dynamics of auto-balancer in accelerating the motor is simulated. The conditions for reducing the non-synchronous motion are explored by simulating the mass and the viscous drag coefficient of the balls. The non-synchronous motion and residual balancing error are suppressed by tuning the viscous drag coefficient and the mass of the balance balls properly.