Abstract: To address the slow convergence and insufficient robustness of blind equalization in underwater acoustic burst communication links, where sparse multipath and impulsive noise coexist, a fast blind equalization method based on the sparse structure of underwater acoustic channels and the maximum correntropy criterion is proposed. The proposed method introduces themaximum correntropy criterion into the constant-modulus cost to suppress the disturbance of large-error samples caused by impulsive noise on gradient updating. A majorization-minimization strategy is then employed to construct a local fast update direction, thereby alleviating the slow convergence of conventional stochastic-gradient methods constrained by small step sizes. Furthermore, by exploiting the sparse structure of underwater acoustic channels, a proportionate normalization mechanism is introduced to enhance the update of dominant taps while suppressing unnecessary perturbations on non-dominant taps, thus achieving fast and stable convergence of the equalizer coefficients. Simulation results show that, under ocean ambient noise and impulsive noise, the proposed method achieves lower symbol error rate and faster convergence than typical blind equalization algorithms such as CMA, MCMA, and MSEI under sparse channel conditions.