The mathematic models and basic theory of constant modulus algorithm (CMA) for blind channel equalization are introduced. An improved algorithm with variable step size is proposed based on CMA. The improved algorithm uses the mean square error (MSE) to obtain the new variable stepsize to solve the contradiction between the convergence rate and accuracy in traditional CMA with fixed step. To smooth the MSE learning curve for easy comparison, an ensemble average technique is used to analyze the performance of convergence with different step sizes. The theoretical analysis and the simulation results show that the improved algorithm is superior to the traditional constant modulus(CM) in terms of convergence speed and residual error.