The paper deals with the coupling of natural boundary element and finite element methods for exterior initial boundary value problems of hyperbolic equations. The governing equation is first discretized in time, leading to a time-step scheme, where an exterior elliptic problem has to be solved in each time step. Second, a circular artificial boundary consisting of a circle with a sufficiently large radius is introduced, the original problem in an unbounded domain is transformed into the nonlocal boundary value problem in a bounded subdomain. Moreover, the natural integral equation and the Poisson integral formula are obtained in the infinite domain outside the circle. The coupled variational formulation is given. The authors discuss the finite element discretization for the variational problem and its corresponding numerical technique, and the convergence for the numerical solutions. Finally, one numerical example is presented to illustrate feasibility end efficiency of the method.