Abstract: To address the sparse system identification problem under noisy input and non-Gaussian output measurement noise, a sparse bias-compensated normalized maximum correntropy criterion (MCC) algorithm is developed in this work. The MCC based adaptive filtering algorithm can eliminate the impact of non-Gaussian measurement noise, and the unbiasedness criterion is introduced to solve the bias estimate issue caused by the noisy input. In addition，the proportionate update scheme is utilized in the proposed algorithm，which can improve the tracking ability by adjusting step-size parameter adaptively. Simulation results confirm that the proposed algorithm shows robustness and steady-state performance for the sparse system identification problem under noisy input and output noise with non-Gaussian environments.