Fast start‐up in adaptive equalization is indispensable in communication systems that require on‐line performance. In this article, a new type of adaptive linear FIR equalizer composed of two FIR filters and called the adaptive Butler–Cantoni (ABC) equalizer is proposed, and speed‐up of convergence in the training mode is attempted. The ABC equalizer consists of a channel estimator and an equalization filter. The channel estimator updates coefficients by the LMS algorithm. At the same time, the variance of the additive noise is computed. Based on these results, the coefficients of the equalization filter are successively derived by the Levinson–Trench algorithm, and the estimated value of the transmitted signal is computed. The computational complexity of the ABC equalizer is proportional to the square of the tap length but is not more than that of the RLS equalizer. By computer simulation, it is demonstrated that the ABC equalizer provides better results than the LMS and RLS equalizers. © 1999 Scripta Technica, Electron Comm Jpn Pt. 3, 82(10): 9–17, 1999