Based on the convergence and stability of the numerical solution of a differential equation, from a solid step Runge-Kutta method, it has considered variable step Runge-Kutta method. Three modified algorithm are discussed. They are step reduced by half Runge-Kutta method, Runge-Kutta-Fehlberg method and Zadunaisky method. At the same time, the accuracy and efficiency of variable step Runge-Kutta method are discussed.%根据一阶常微分方程数值解的收敛性与稳定性，从固步长的Runge-Kutta法出发，考虑变步长的Runge-Kutta法，讨论了3种改进算法，即折半步长Runge-Kutta法、Runge-Kutta-Fehlberg法和Zadunaisky方法。并且分别讨论了3种变步长的Runge-Kutta法的精度及效率。
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