Speech communication in real-world environments requires adaptation to changing acoustic conditions. How the human auditory cortex adapts as a new noise source appears in or disappears from the acoustic scene remain unclear. Here, we directly measured neural activity in the auditory cortex of six human subjects as they listened to speech with abruptly changing background noises. We report rapid and selective suppression of acoustic features of noise in the neural responses. This suppression results in enhanced representation and perception of speech acoustic features. The degree of adaptation to different background noises varies across neural sites and is predictable from the tuning properties and speech specificity of the sites. Moreover, adaptation to background noise is unaffected by the attentional focus of the listener. The convergence of these neural and perceptual effects reveals the intrinsic dynamic mechanisms that enable a listener to filter out irrelevant sound sources in a changing acoustic scene.