Abstract: We first present the eighth-order NAD method for solving the acoustic equation by introducing the nearly analytic discrete operator with high-order accuracy.Then the analysis of numerical errors and results of computational efficiency show the eighth-order NAD method has high numerical accuracy,high computational efficiency and low computing storage,compared against the fourth-order Lax-Wendroff correction (LWC) scheme and the eighth-order LWC scheme.At last,we apply the eighth-order NAD method to model the seismic wave-field propagating in complex heterogeneous three-layer medium and Marmousi model.The numerical results illustrate that the new method can effectively suppress numerical dispersion.And the eighth-order NAD method has strong application of seismic wave simulation.