By the universal D'Alembert's principle in variable-mass mechanical system, we obtain Mac-Millan type equations in quasi-coordinates for the variable-mass mechanical system with non-holonomic constraints, and give all corollaries of our results. Finally, an example is given to illustrate its application. 本文根据变质量力学系统的万有D'Alembert原理得到了变质量高阶非完整力学系统在准坐标下的Mac-Millan型方程,然后导出本结果的几个推论并举例说明该方程的应用。