We study the global existence and uniqueness of a solution to an initial boundary value problem for the nonlinear wave equation with the p-Laplacian operator u tt −div |∇u| p−2 ∇u −Δu t g x, u f x . Further, the asymptotic behavior of solution is established. The nonlinear term g likes g x, u a x |u| α−1 u − b x |u| β−1 u with appropriate functions a x and b x , where α > β ≥ 1.