For the identification of the multiple-input controlled autoregressive systems with unknown time-delays, a greedy orthogonal least squares identification algorithm based on the Householder transformation is discussed. Since the time-delays are unknown, an over-parameterization identification model with a sparse parameter vector can be obtained by setting an input regression length. In order to avoid computing the inverse of the high-dimensional covariance matrix in the least squares algorithm, an orthogonal least squares algorithm based on the Householder transformation is derived and a greedy criterion based on the Householder transformation is derived to improve the identification efficiency and reduce the identification cost. The proposed algorithm can effectively estimate the sparse parameter vector with a small amount of sampled data. Finally, the time-delays are estimated according to the structure of the sparse parameter vector. A simulation example is used to illustrate the effectiveness of the proposed algorithm.