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The maximum correntropy criterion (MCC) algorithm has popularly been used in suppressing impulsive noise. It mainly relies on the choice of step size and kernel width. With the study of step size, this paper proposes a novel algorithm that updates the step size based on constructing a variable step size function that uses the moving weighted average algorithm to keep performance stable and sigmoid function to speed the convergence rate. The proposed algorithm is robust against impulsive noises and generates a large step size to accelerate the convergence in iteration beginning, and system mutation makes the system identification performance more stable when the error is small. Based on the improved variable kernel width maximum entropy criterion (IVKW‐MCC) algorithm, which overcomes the shortcoming of how to choose a reliable kernel width in the MCC algorithm, simulation results are compared with other MCC algorithms under impulsive noise interference. Simulations in the system identification scenarios show that the proposed algorithm has better performance in improving the convergence speed over other algorithms. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]