Blind equalization is a technique for adaptive equalization of a communication channel without the use of training sequence. Although the constant modulus algorithm (CMA) is one of the most popular adaptive blind equalization algorithms, because of using fixed step size it suffers from slow convergence rate. A novel enhanced variable step size CMA algorithm (VSS-CMA) based on autocorrelation of error signal has been proposed to improve the weakness of CMA for application to blind equalization in this paper. The new algorithm resolves the conflict between the convergence rate and precision of the fixed step-size conventional CMA algorithm. Computer simulations have been performed to illustrate the performance of the proposed method in simulated frequency selective Rayleigh fading channels and experimental real communication channels. The obtained simulation results using single carrier (SC) IEEE 802.16-2004 protocol have demonstrated that the proposed VSS-CMA algorithm has considerably better performance than conventional CMA, normalized CMA (N-CMA) and the other VSS-CMA algorithms.