In this paper, we investigate the superconvergence property of the numerical solution to a quadratic elliptic control problem by using mixed finite element methods. The state and co-state are approximated by the order k = 1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We prove the superconvergence error estimate of \(h^{\tfrac{3} {2}} \) in L 2-norm between the approximated solution and the average L 2 projection of the control. Moreover, by the postprocessing technique, a quadratic superconvergence result of the control is derived.