To adapt to the sparsity of some sparse systems in system identification, a novel modified recursive least squares algorithm is proposed. This algorithm utilizes the output error to control the value of forgetting factor, which deals with the contradiction between convergence rate and stationary misadjustment. In addition, through the introduction of zero attractor in parameters' iterations, the proposed algorithm improves the convergence rate of zero and near-zero parameters dominating sparse systems. The simulation results indicate that the algorithm proposed in this paper can effectively strengthen the accuracy of sparse system identification.