Abstract: In this paper, the mean square error (MSE) criterion used in the In this paper, the mean square error (MSE) criterion used in the constant modulus algorithm (CMA) is modified by the maximum correntropy criterion (MCC) to solve the problem of performance degradation of the CMA blind equalization algorithm under impulse noise environment, and then the a constant modulus blind equalization algorithm based on MCC is derived, which is referenced as MCC_CMA. By utilizing the constant modulus property of the communication signals, the proposed algorithm first obtains the modulus difference signal between the transmitted signal and the equalizer output signal, and then the iterative error adjustment term is achieved by maximizing the correntropy of the modululs difference signal, thus the problem of the performance degradation of the traditional high-order statistics based algorithms under impulse noise environment is avoided. Under Gaussian noise environment and two kinds of impulse noise environment: α-stable distribution and mixture Gaussian distribution, the simulation experiments of channel equalization problem show that the MCC_CMA algorithm not only can obtain faster convergence speed, lower residual intersymbol interference and bit error ratio without relying on the prior knowledge of noise, comparing with the classical adaptive constant modulus blind equalization algorithm; but also has good robustness, that is, it can get good equalization results in impulse noise environments with different impulsiveness.