A novel variable step size constant modulus algorithm (VSS-CMA) employing cross correlation between channel output and error signal has been proposed as a solution to the problem of slow convergence of CMA algorithm. The new algorithm resolves the conflict between the convergence rate and low steady state error of the fixed step-size conventional CMA algorithm. Computer simulations have been performed to verify the performance of the proposed method in frequency selective Rayleigh fading channels. The proposed technique has been compared with the popular non-blind equalizer, Least Mean Squares (LMS) algorithm, and blind equalizer, the conventional CMA and Zhao's VSS-CMA as benchmarks. The obtained simulation results have demonstrated that the proposed VSS-CMA algorithm has considerably better performance than the conventional CMA and Zhao's VSS-CMA blind equalization algorithms, and the conventional LMS non-blind equalization algorithm.