This paper deals with the generalized discrete Shannon convolutional differentiator (GDSCD) for solving seismic velocity-stress equation. The first-order convolution differentiators are provided. An efficient method is proposed to optimize the coefficients of the convolution differentiator. A series of optimal coefficients are obtained for various operator lengths and sampling rates per shortest wave length. The operator accuracy is discussed through filter response. A comparison with various numerical methods and numerical experiments show that the new designed staggered grid convolution differentiator has high accuracy and efficiency for seismic wave modeling.