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Abstract In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal L 2 $L^{2}$ -norm error estimates. The approximate orders for the state, costate, and control variables are O ( h 2 ) $O(h^{2})$ in the sense of L 2 $L^{2}$ -norm. Furthermore, we derive H 1 $H^{1}$ -norm error estimates for the state and costate variables. Finally, we give some conclusions and future works.