In the pulse compression radar using linear frequency modulation (LFM), the sidelobe suppression signal processing is very important to overcome an effect that may mask smaller targets or maybe mistaken as separate targets. This paper considers a novel framework of the sidelobe suppression for linear frequency modulation signal (LFM) at a receiver when existing internal receive noise. In pulse compression for LFM signal, there exist not only range mainlobe components but also range sidelobe components in the matched filter output. It is necessary to effectively suppress the sidelobe components at the receiver of radar. This paper presents variability index (VI)-threshold operation based on the wavelet transform to further reduce these range sidelobes, and then analyzes it compared to the conventional window method. The results show that the proposed method is very effective in suppression of sidelobes components for LFM signal. It also indicates that this method gives better a peak to sidelobe ratio (PSR) performance than other methods for the sidelobe suppression.