Dynamic stability of badminton is one of the important conditions to ensure stable rotation and control the landing point, but in practice the badminton motion is more complex. In order to reveal the physical phenomenon of badminton sport, this article establishes a mathematical model for badminton flight rotational about all time-varying parameters of badminton movement, and combined with the stability definition of Lyapunov motion, the mathematical definition for the stability of badminton movement is given; and further research the reasons which influence the stability of badminton movement. By analyzing, it can be derived the relationship of badminton composition factors influence on the stability of badminton, criterion of badminton movement stability, and also point out the criterion range. Through calculation, the judgement results are consistent with the experiment results.