The problem of identifying the solution (k(x, t),U(x, t)) in an inverse semilinear wave problem is considered. It is shown that under certain conditions of data ϕ, ψ, there exists a unique solution (k(x, t),U(x, t)) of this problem. Furthermore a numerical algorithm for solving the inverse semilinear wave problem is proposed. The approach for this inverse problem is given by using the semi-discretisation method. A polynomial function is proposed to approximate U(x, t) then the finite difference method is applied to approximate unknown k(x, t). Numerical results show efficiency of our method.