Abstract: Rayleigh surface wave has been used to research the character of shallow subsurface widely, and the real geological medium is close to viscoelastic media. This paper models Rayleigh wave in viscoelastic media with planar free surface by using the staggered-grid finite-difference method based on the generalized standard linear body. And we compared the results of the viscoelastic media with the elastic one. In this paper the Levenberg-Marquarat algorithm is adopted to compute the relaxation time to fitting the constant Q model firstly. Acoustic-elastic boundary approximation method is used to implement free surface conditions. The condition that transverse stress on and under the free surface remain continuous is considered by keeping the shear modulus unchanged. And for other boundaries the unsplit multiaxial convolutional perfectly matched layer is chosen to absorb waves. Then the wave fields are calculated in several typical models. The comparisons of numerical and analytical solutions confirm the veracity and validity of the method in this paper. And the computed results indicate that viscoelasticity can influence the surface wave dispersion. So the viscoelastic factors should be considered in the surface wave exploration.