We construct multigrid methods for an elliptic distributed optimal control problem that are robust with respect to a regularization parameter. We prove the uniform convergence of the W -cycle algorithm and demonstrate the performance of V -cycle and W -cycle algorithms in two and three dimensions through numerical experiments.Date: September 22, 2018. 1991 Mathematics Subject Classification. 49J20, 65N30, 65N55, 65N15. Key words and phrases. elliptic distributed optimal control problem, saddle point problem, P 1 finite element method, multigrid methods.