The identification problem of the multiple-input single-output controlled autoregressive systems with unknown time-delays and finite sampled data is studied. A linear equation set is said to be undetermined if the number of equations is less than that of unknown variables. Traditional methods such as the least squares algorithm cannot provide the unique solution for an undetermined equation set because it is an NP-hard problem. Based on the compressed sensing theory, a new orthogonal matching pursuit(OMP) algorithm is proposed for estimating the time-delays of the input channels and the system parameters. The simulation results show the effectiveness of the proposed method.