This paper aims to construct a two-grid scheme for distributed optimal control governed by semilinear elliptic equations. The state and co-state are approximated by the P_0^2-P_1 pair and the control variable is approximated by piecewise constant functions. First, a priori error estimates for the control variable, the state variables and the co-state variables are obtained. Second, a two-grid P_0^2-P_1 mixed finite element scheme is presented and the corresponding error is analyzed. Finally, a numerical example demonstrating our theoretical results is also presented in this paper.