This paper deals with the performance comparison of adaptive equalization algorithm, CMA and MMA, that is used for the minimization of the distortion and noise effect in the communication channel at receiver.. We confirmed the application possibilities of the point to point or point to multipoint digital transmission technologies by analyzing the performance of MMA which is changing the error function of CMA that is the possible algorithm of fast equalization by relatively simple arithmatic computation compared to the other method. In CMA algorithm, we need the PLL for the amplitude compensation only and not possible to phase compensation inherently. But in MMA algorithm, we confired that the amplitude and phase of received signal can be compensated by computer simulation. For the comparison of algorithm, we used the essential performance index, convergence characteristics and residual isi. The result of performance comparison of algorithms, the MMA has good in convergence characteristic and the CMA has good in residual isi that is used for the amplitude compensation.