For the identification of a class of closed-loop systems with unknown time-delays in both the control plant and the feedback controller, an instrumental variable based compressed sampling matching pursuit method is developed. By using the instrumental variable identification idea to modify the compressed sampling matching pursuit algorithm, the sparse parameter vector of the overparameterized identification model is firstly estimated. Then the estimates of the control plant parameters and the time-delays can be extracted from the estimated parameter vector, and the parameters of the feedback controller can be obtained by using the model equivalence principle. Simulation results show that the proposed method can effectively estimate the parameters and time-delays for the class of closed-loop systems with only a few iterations.