In this study we used functional near-infrared spectroscopy (fNIRS) to investigate neural responses in normal-hearing adults as a function of speech recognition accuracy, intelligibility of the speech stimulus, and the manner in which speech is distorted. Participants listened to sentences and reported aloud what they heard. Speech quality was distorted artificially by vocoding (simulated cochlear implant speech) or naturally by adding background noise. Each type of distortion included high and low-intelligibility conditions. Sentences in quiet were used as baseline comparison. fNIRS data were analyzed using a newly developed image reconstruction approach. First, elevated cortical responses in the middle temporal gyrus (MTG) and middle frontal gyrus (MFG) were associated with speech recognition during the low-intelligibility conditions. Second, activation in the MTG was associated with recognition of vocoded speech with low intelligibility, whereas MFG activity was largely driven by recognition of speech in background noise, suggesting that the cortical response varies as a function of distortion type. Lastly, an accuracy effect in the MFG demonstrated significantly higher activation during correct perception relative to incorrect perception of speech. These results suggest that normal-hearing adults (i.e., untrained listeners of vocoded stimuli) do not exploit the same attentional mechanisms of the frontal cortex used to resolve naturally degraded speech and may instead rely on segmental and phonetic analyses in the temporal lobe to discriminate vocoded speech.