This paper considers the parameters and input time delays identification for multiple-input single-output controlled auto-regressive moving average (MISO C-ARMA) systems with unknown input time delays. The parameterized model can be treated as a sparse system. According to the hierarchical identification principle, gradient search principle and matching pursuit idea, a gradient pursuit iterative-based algorithm is presented to simultaneously estimate parameters and time delays of MISO C-ARMA systems. The proposed algorithm can reduce the computational cost compared with the orthogonal matching pursuit iterative-based algorithm. Finally, a simulation example is given to show the effectiveness of the proposed algorithm.