Abstract: The inverse problems, with a bright future are in the forefront of both theoretical and applicational science researches within the international scope. Especially the studies in exploring the variations of physical parameters in closing objects by using acoustic wave or seismic wave methods are paid great attention to, because of its relation with many domains such as mathematics, mechanics, physics and computer science and its wide applications in geological exploration, engineering and medicine. This sort of problems can be included in the category of determining coefficients terms in a partial differential equations in mathematics. The previous researches are based on the elastic media model. A model of coefficient inverse problems of wave equation in viscoelastic media is proposed in this paper, which describes characteristics of geological media more truly. The finite element method and the least-squares inversion process are used to solve the inverse question of plane viscoelastic wave equation in the frequency domain. A numerical perturbational algorithm has also been employed for obtaining the gradient matrix quickly and accurately. Singular Values Decomposition (SVD) produces significant improvements in computational precision. Based on above-mentioned studies, the authors have compiled the computational programs. Some numerical examples, showing the validity and practicality of the model and the numerical algorithm, are also given.