This paper deals with the FC-MMA (Fast Convergence-Multi Modulus Algorithm) which is improving the convergence characteristics of the MMA (Multiple Modulus Algorithm) adaptive equalization algorithm that is used for the minimization of the intersymbol interference which occurs in the time dispersive communication channel. In the time varying charateristics and the abnormal situation like as outage of the communication channel, the adaptive equalizer needs to adapting the new environment more rapidly. For this problem, the residual isi and the maximum distortion performance index which are meaning the convergence characteristics are widely adapted in the adaptive equalizer. The 16-QAM signal is transmitted and it was confirmed that the proposed algorithm, the FC-MMA has the fast convergence performance such as in the 1.75 times fast in residual isi and 2.5 times fast in the maximum distortion in order to reaching the steady state compare to the MMA algorithm in the same channel environment by the computer simulation.