On the basis of Carcione’s theories of viscoelasticity and anisotropy, two-dimensional, three-component, first-order velocity-stress wave equations of viscoelastic tilted transversely isotropic(viscoelastic TTI) media are presented and a rotated staggered grid any-order finite-difference scheme is used to numerically solve the equations. Equations of the perfectly matched layer(PML) are derived for the wave equations in viscoelastic TTI media and the rotated staggered grid any-order finite-difference scheme is also used to solve these equations. The results of numerical modeling indicate that the modeling precision is high and the absorbing boundary condition is good in the viscoelastic TTI media, and high-precision snapshots of wave field and synthetic seismograms can be obtained, and they can reflect the characteristic of viscoelasticity and anisotropy.