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High frequency surface wave radar (HFSWR) has been successfully developed for early warning and remote sensing. However, the ionospheric clutter is a difficult challenge that can make HFSWR system inefficient. The Generalized Side-lobe Canceller (GSC) has been proved to be an effective algorithm for clutter suppression in theory, but it suffers from the performance degradation for some non-ideal conditions in practice. The most intolerable shortcoming is the signal to noise ratio (SNR) loss caused by the residual signal in the secondary data. In this paper, a knowledge-based GSC (KB-GSC) method has been proposed via an adaptive single notch filter design to reject the residual signal for reducing the SNR loss. The feasibility and availability has been demonstrated by measured data.