For the identification of the multiple-input output-error systems with unknown time-delays, an orthogonal matching pursuit iterative algorithm based on the auxiliary model is proposed. Due to the unknown time-delays of each input channel, a highly dimensional identification model with a sparse parameter vector is derived by setting an input regression length and using the overparameterization. Then, based on the auxiliary model idea and the orthogonal matching pursuit(OMP) algorithm, the parameter vector and the output of the auxiliary model are interactively estimated in each iteration, that is, the OMP algorithm is applied to obtain the estimation of the parameter vector, the auxiliary model output is computed by using the estimated parameters, and then the parameter estimation updated by the information vector where the unmeasurable information items are repaced by the auxiliary model outputs. Finally, the time-delays are estimated according to the sparse characteristic of the parameter vector. The proposed method can simultaneously estimate the parameters and time-delays from a few sampled data. A simulation example is used to illustrate the effectiveness of the proposed algorithm.