In this talk, we first show the exact boundary  controllability  for  a coupled system of wave equations with Neumann boundary controls. In order to establish the  corresponding observability inequality, we introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only  on the continuity of projection with respect to a weaker norm,  which is obviously true in many cases of application. We next observe that the  Neumann boundary value problem  can be served   to obtain the exact boundary controllability with coupled Robin boundary controls. Finally, in the case of less boundary controls, we show the non exact boundary controllability with both Neumann and coupled Robin boundary controls, respectively.