Selectively attending to task-relevant sounds whilst ignoring background noise is one of the most amazing feats performed by the human brain. Here, we studied the underlying neural mechanisms by recording magnetoencephalographic (MEG) responses of 14 healthy human subjects while they performed a near-threshold auditory discrimination task vs. a visual control task of similar difficulty. The auditory stimuli consisted of notch-filtered continuous noise masker sounds, and of 1020-Hz target tones occasionally () replacing 1000-Hz standard tones of 300-ms duration that were embedded at the center of the notches, the widths of which were parametrically varied. As a control for masker effects, tone-evoked responses were additionally recorded without masker sound. Selective attention to tones significantly increased the amplitude of the onset M100 response at 100 ms to the standard tones during presence of the masker sounds especially with notches narrower than the critical band. Further, attention modulated sustained response most clearly at 300–400 ms time range from sound onset, with narrower notches than in case of the M100, thus selectively reducing the masker-induced suppression of the tone-evoked response. Our results show evidence of a multiple-stage filtering mechanism of sensory input in the human auditory cortex: 1) one at early (100 ms) latencies bilaterally in posterior parts of the secondary auditory areas, and 2) adaptive filtering of attended sounds from task-irrelevant background masker at longer latency (300 ms) in more medial auditory cortical regions, predominantly in the left hemisphere, enhancing processing of near-threshold sounds.