In this paper, {\it optimize-then-discretize}, variational discretization and the finite volume method are applied to solve the distributed optimal control problems governed by second order hyperbolic equation. A semi-discrete optimal system is obtained. We prove the existence and uniqueness of the solution for the semi-discrete optimal system and obtain the optimal order error estimates in continuous $L^\infty(J;L^2)$ and $L^\infty(J;H^1)$-norm. Numerical experiments are presented to test these theoretical results.