<p>Though largely ignored in the past, aperiodic (i.e., irregular, non-oscillatory) activity is emerging as an important element of the electroencephalography (EEG) signal. Certain characteristics of broadband aperiodic activity have been shown to reflect dynamic neurophysiological states that are sensitive to cognitive task demands and predictive of individual differences in cognitive capacity. In the current study, we test whether aperiodic neural activity can be used to index cognitive effort during speech comprehension in older listeners. Older adults with varying hearing acuity (<i>N</i> = 48) listened to sentences in quiet and in background noise while EEG was recorded. Consistent with listening effort, aperiodic neural activity was sensitive to increased acoustic challenge such that the aperiodic slope flattened and offset was reduced with increasing noise. Moreover, noise-induced changes in aperiodic activity were greater for older adults with poorer hearing acuity. In an age-comparative analysis using additional data from young normal hearing adults (<i>N</i> = 35), age-related reductions in aperiodic slope and offset were observed, replicating past work, while sensitivity to background noise was observed in both age groups. These findings highlight the importance of considering aperiodic EEG activity in assessing cognitive listening effort specifically, and in challenging cognitive tasks more generally.</p>