This paper discusses the convergence properties of optimal control of a system describedby an elliptic partial differential equation on a perturbed domain.Assume that the perturbed domain \Omega_ε can be characterized by a small parameter ε.Then the optimal control,v_ε~*,and the corresponding optimal solution,u_ε~*,depend on the perturbed parameter ε.Itis shown that u_ε~* and v_ε~* converge to u_0~* and v_0~* respectively as ε goes to 0,where v_0~* andu_0~* are the optimal control and the optimal solution of the system on the unperturbeddomain \Omega_0.