This paper is concerned with the DW-MCMA(Dual Weight vector Modified Constant Modulus Algorithm) adaptive equalization algorithm using the dual weight vector in order to improve the convergence characteristic and residual inter-symbol interference which are used as the performance index for an adaptive equalizer. The equalizer is used to reduce the distortion caused by the inter-symbol interference on the wireless and the wired band-limited channel that connect the transmitting system and receiving system. The CMA is widely known as the representative algorithm for equalization. In order to transmitting the mass information with a high speed through the channels, a fast convergence speed in the equalizer performance that is able to minimize overhead needed for equalization is acquired. In this paper, By the computer simulation, we confirmed that the proposed DW-MCMA has the faster convergence speed and the smaller residual inter-symbol interference than the conventional CMA and MCMA.