Abstract: We propose a sparse bias-compensated least mean logarithmic square (LMLS) algorithm to solve the low precision problem of the LMLS algorithm in sparse system identification with noisy input. We derive the bias compensation term by using the unbiasedness criterion to compensate the bias caused by input noise, and construct a bias-compensated LMLS (BCLMLS). To fully utilize the prior knowledge on the sparse system, we introduce the correntropy-induced metric as a sparse penalty constraint to optimize the proposed BCLMLS algorithm. The simulation results demonstrate that the proposed algorithm has a good steady-state performance in solving sparse system identification problems with noisy inputs.