Abstract: One of many problems geophysicists concern with and endeavor to solve in a long time is lacking of new methods that can well balance the incompatible relation between accuracy and computation efficiency in seismic modeling. In order to solve this problem and correctly recognize the geophysical response of the subsurface structures, we derived a kind of numerical method named staggered-grid convolutional differentiator to solve the one-order velocity-stress equation in elastic media based on discrete Shannon singular kernel theory, whose optimal coefficients are obtained with nonlinear optimization method. Accuracy comparison between optimal staggered-grid convolutional differentiator and staggered-grid finite differentiators with different lengths indicates that the accuracy of the eight-order scheme differentiator proposed in this paper is comparable with 16-order staggered-grid finite difference, which, in other words, means that optimal staggered-grid convolutional differentiator has fewer points per wavelength when the two differentiators have the same length. Numerical modeling in Corner-Edge model also demonstrates that the optimal staggered-grid convolutional difference method is of highly efficiency and robustness, which can be chosen as an alternative method to compute the wavefield in complex media.