Resting-state alpha brain rhythms provide a foundation for basic as well as higher-order brain processes. Research suggests atypical maturation of the peak frequency of resting-state alpha activity (= PAF) in autism spectrum disorder (ASD). The present study examined resting-state alpha activity in young school-aged children, obtaining magnetoencephalographic (MEG) eyes-closed resting-state data from 47 typically developing (TD) males and 45 ASD males 6.0 to 9.3 years old. Results confirmed a higher PAF in ASD versus TD, and demonstrated that alpha power differences between groups were linked to the shift of PAF in ASD. Additionally, a higher PAF was associated with better cognitive performance in TD but not ASD. Finding thus suggested functional consequences of group differences in resting-state alpha activity.