We consider the numerical approximation for two types of optimal control problems governed by elliptic interface equations. We adopt the variational discretization concept to discretize the optimal control problems, and apply extended finite element methods for the elliptic equations to discretize the corresponding state and adjoint equations. Optimal error estimates are derived for the optimal state, co-state and control. Numerical results verify the theoretical results. This is a joint work with Tao Wang and Chaochao Yang.