  We analyze a fully discrete scheme based on the discontinuous (in time)
Galerkin approach, which is combined with conforming finite element subspaces
in space, for the distributed optimal control problem of the three-dimensional
Navier-Stokes-Voigt equations with a quadratic objective functional and box
control constraints. The space-time error estimates of order
$O(\sqrt{\tau}+h)$, where $\tau$ and $h$ are respectively the time and space
discretization parameters, are proved for the difference between the locally
optimal controls and their discrete approximations.
