In adaptive equalizers based on least mean squares (LMS) algorithms, the convergence rate is determined by the convariance matrix of an input signal. When the eigenvalue spread of the convariance matrix is close to unity, the convergence rate is quite fast. In this paper, for fast convergence of LMS-based adaptive equalizers we propose a modified reference signal pertinent to the statistical channel. From the theoretical analysis and computer simulation, it is shown that the proposed modification method is quite effective for fast convergence of LMS-based adaptive equalizers.