In wireless communication systems, the conventional constant modulus algorithm incurs artificial error and steady state misadjustment. In this study, an improved constant modulus algorithm (ICMA) and its generalized form are proposed for blind equalization. The ICMA utilizes the clustering function of Gaussian function to efficiently suppress this artificial error and steady state misadjustment at the cost of reduction in the sample usage rate. Moreover, the generalized form of the ICMA is developed to ensure the sample usage rate while the good performances of the ICMA are maintained. Simulation results illustrate better equalization performances of the ICMA and generalized ICMA, as compared to the classical constant modulus algorithm.