Abstract <p>In this paper, we will give a new Crank–Nicolson mixed covolume method for parabolic optimal control problems. The state and costate variables are approximated by the lowest order Raviart–Thomas element and the control variable is approximated by piecewise constant function, while Crank–Nicolson scheme is ultilized for temporal discretization. We derive the priori error estimates for the control variable, the state and the costate variables.</p>