This paper deals with the generalized discrete Shannon convolutional differentiator(GDSCD) for solving seismic velocitystress 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.