It is often assumed that the benefit of hearing aids is not primarily reflected in better speech performance, but that it is reflected in less effortful listening in the aided than in the unaided condition. Before being able to assess such a hearing aid benefit the present study examined how processing load while listening to masked speech relates to inter-individual differences in cognitive abilities relevant for language processing. Pupil dilation was measured in thirty-two normal hearing participants while listening to sentences masked by fluctuating noise or interfering speech at either 50% and 84% intelligibility. Additionally, working memory capacity, inhibition of irrelevant information, and written text reception was tested. Pupil responses were larger during interfering speech as compared to fluctuating noise. This effect was independent of intelligibility level. Regression analysis revealed that high working memory capacity, better inhibition, and better text reception were related to better speech reception thresholds. Apart from a positive relation to speech recognition, better inhibition and better text reception are also positively related to larger pupil dilation in the single-talker masker conditions. We conclude that better cognitive abilities not only relate to better speech perception, but also partly explain higher processing load in complex listening conditions.