Abstract: In order to perfectly analyze the dynamics problem by numerical manifold method (NMM), adopts the Newmark method of dynamic finite element method to improve the algorithm in original NMM on the basis of analyzing the solution idea of dynamics problem in NMM. The improved method has three evident advantages over the original one: (1) The solution of this method is convergent without any condition, when selecting suitable parameters; (2) The time step that can be adopted in this method is much longer than that in the original one; (3) The damp effect in the dynamics problem is fully considered. In the end, a calculation example is adopted to illustrate that the improved numerical manifold method can perfectly simulate the whole process of rock failure under impact load, which overcomes the deficiency of FEM in simulating the block movement of rock after failure.