Abstract: High data rate communication over limited bandwidth or multi-path channels suffers severe distortion due to the Inter-Symbol Interference (ISI). Constant Modulus blind equalization Algorithms (CMA) are widely used for mitigating this phenomenon. But for higher-order no constant amplitude modulations, CMA works less effective for its large residual error. A simple modified error function which is suitable for variable constellation is proposed for better convergence performance. The new algorithm is well verified by theoretic analysis and numerical simulations, and the theoretic analysis and simulations show that the new algorithms residual error is much less than the origin algorithms in MQAM and MAPSK modulation systems and the new algorithm is suitable for applications under these conditions.