Although individual differences in adult language processing are well-documented, the neural basis of this variability remains largely unexplored. The current study addressed this gap in the literature by examining the relationship between resting state alpha activity and individual differences in auditory language comprehension. Alpha oscillations modulate cortical excitability, facilitating efficient information processing in the brain. While resting state alpha oscillations have been tied to individual differences in cognitive performance, their association with auditory language comprehension is less clear. Participants in the study were 80 healthy adults with a mean age of 25.8 years (SD = 7.2 years). Resting state alpha activity was acquired using electroencephalography while participants looked at a benign stimulus for 3 min. Participants then completed a language comprehension task that involved listening to ‘syntactically simple’ subject-relative clause sentences and ‘syntactically complex’ object-relative clause sentences. Pupillometry measured real-time processing demand changes, with larger pupil dilation indicating increased processing loads. Replicating past research, comprehending object relative clauses, compared to subject relative clauses, was associated with lower accuracy, slower reaction times, and larger pupil dilation. Resting state alpha power was found to be positively correlated with the pupillometry data. That is, participants with higher resting state alpha activity evidenced larger dilation during sentence comprehension. This effect was more pronounced for the ‘complex’ object sentences compared to the ‘simple’ subject sentences. These findings suggest the brain's capacity to generate a robust resting alpha rhythm contributes to variability in processing demands associated with auditory language comprehension, especially when faced with challenging syntactic structures. More generally, the study demonstrates that the intrinsic functional architecture of the brain likely influences individual differences in language comprehension.