Early convolutional differentiators are all based on the Fourier transformation,their precision is a little higher than that of four-order finite difference.For improving the precision and efficiency of seismic modeling,a new modeling approach（Convolutional Forsyte Polynomial Differentiator Method,CFPD）is developed in this paper by using optimized convolutional operators for spatial differentiation and staggered-grid finite-difference for time differentiation in wave equation computation.The solution of this new method is much close to the exact value,and the precision is nearly equal to that of 16-order finite difference.Viscous-elastic wave equation can better explain wave phenomena of the true earth media.This paper applies the CFPD method to model 2-D viscous-elastic seismic wave field for the first time,and further derives the first-order velocity-stress discreate equations for viscous-elastic media.The numerical results show that the algorithm can bring reliable outcomes with high precision and fast speed,and viscous-elastic modeling is much efficient.