This paper introduces a systolic array structured adaptive decision feedback equalizer (DFE) based on extended QR-RLS (QR-decomposition-based Recursive Least Squares) algorithm. In the wireless mobile communication systems, the fast time-varying channel could be experienced, so that high-speed convergence along with precise tracking ability is a crucial requirement for the equalizers. To cope with this, the QR-RLS algorithm has been considered as an adaptation apparatus satisfying these requisitions with showing numerical stability in fixed-point operation. In the aspect of realization, the QR-RLS algorithm could be realized in a form of systolic array, which gives an opportunity of utilizing the parallel pipelined processing. Even the computational complexity can be reduced by avoiding the square-root operations. However, the conventional QR-RLS approach demands the extra weight extraction process, so that the equalization can be hardly accomplished by a full pipelined process. Against this difficulty, this paper exploits the extended QR-RLS algorithm to build up the systolic array structured DFE in efficient. In addition to affirmative features such as the fast convergence and the superb tracking ability, the proposed DFE architecture based on the extended QR-RLS yields a capability of full pipeline process from the input acquisition till the weight update without involving undesirable square-root operations.