Age-related hearing loss is not only a disorder of the inner ear, but also of the brain, which has to complement the degraded speech input while incurring structural and functional declines. This ‘central’ hearing loss manifests itself in various aspects of the brain, such as integrity of its structure, but also in its functional properties. For example, aging is associated with a change in absolute and relative oscillatory power in different frequency bands of the human electroencephalogram (EEG), which have consistently been found to be related to speech comprehension. Specifically, oscillatory power changes in the alpha frequency band (8-12 Hz) are related to inhibition of irrelevant stimulus information. In the current study, while their EEG from 128 electrodes was recorded, N = 24 older adults (age 65-80) with varying degrees of sensorineural hearing loss listened to an audiobook in four different background noise conditions, embedded in a 2-by-2 design: The number of talkers as well as the signal-to-noise ratio were varied. We tested to what extent the modulation of alpha oscillations as a proxy for older adults’ inhibition of irrelevant stimulus information would predict speech understanding in these challenging listening environments. Additionally, inhibition was measured behaviourally via a Flanker task. The results showed that the behavioural measurement of inhibition predict the ability to follow a target speaker in multi-talker background noise. However, this was not related to the modulation of alpha oscillations during the task. Also, while we found that even within a sample of older adults, age predicted the amount of alpha desynchronization over the time course of a trial, this in turn did not predict the ability to follow the target stimulus. The results suggest that inhibition is a relevant ability for suppressing background noise, but that the function of alpha oscillations in this context warrants a more thorough investigation.