This paper proposes an efficient equalizer architecture using the tap allocation memory based on the Kalman algorithm. The equalizer for HDTV channel needs many taps to be adequate for a long delay multipath, which causes a high computational complexity to update the coefficient. We propose a new method that the energy of tap and the channel delay length are observed during training period and then the taps having negligible energy are gradually excluded from the coefficient update. The remaining taps form a new coefficient vector by the tap allocation memory that reduces the computational complexity without any performance degradation. The proposed structure is simulated on the channel of North American terrestrial High Definition Television (HDTV).