A new variable step size (VSS) control technique employing cross correlation between channel output and error signal has been proposed as a solution to the problem of slow convergence of blind and non-blind equalization algorithms. The new method resolves the conflict between the convergence rate and low steady state error of the fixed step-size conventional blind and non-blind equalization algorithms, such as Constant Modulus Algorithm (CMA) and Least Mean Squares (LMS) 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 equalizers, LMS and Recursive Least Squares (RLS) algorithms, and blind equalizers, the conventional CMA, Zhao's VSS-CMA and Demir's VSS-CMA as benchmarks'. The obtained simulation results have demonstrated that the proposed VSS-CMA and VSS-LMS algorithms have considerably better performance than the conventional CMA, Zhao's VSS-CMA and Demir's VSS-CMA blind equalization algorithms, and the conventional LMS non-blind equalization algorithm.