The MCMA adaptive blind equalization algorithm has a excellent phase correction capabilities in addition to channel amplitude equalization, but has an inevitable error by mismatching between the original constellation points in arriving at the perfect equalization since unique new type constellation points are used as desired response instead of original constellation points and follows the slow convergence speed of CMA. In this paper, We propose an adaptive blind equalization algorithm with dual-mode, which has decision regions. Inside the decision regions, it operates as considering the moudlus of original data symbol point and outside the decision region, it operates as considerin gthe modulus of new constellation points. The proposed algorithm has a lower error in the steady state and rapid convergence speed toward steady state using the original data symbol points instead of new constellation points in the decision regions. From computer simulation, we confirm that the propposed algorithm has the performance superiority in residual ISI, convergence speed compared with the cnventional adaptive blind equalization algorithms, CMA, MCMA, Stop-and-Go algorithm.