Children with sensorineural hearing loss show considerable variability in spoken language outcomes. The present study tested whether specific deficits in supra-threshold auditory perception might contribute to this variability. In a previous study by Halliday, Rosen, Tuomainen, and Calcus [(2019). J. Acoust. Soc. Am. 146, 4299], children with mild-to-moderate sensorineural hearing loss (MMHL) were shown to perform more poorly than those with normal hearing (NH) on measures designed to assess sensitivity to the temporal fine structure (TFS; the rapid oscillations in the amplitude of narrowband signals over short time intervals). However, they performed within normal limits on measures assessing sensitivity to the envelope (E; the slow fluctuations in the overall amplitude). Here, individual differences in unaided sensitivity to the TFS accounted for significant variance in the spoken language abilities of children with MMHL after controlling for nonverbal intelligence quotient, family history of language difficulties, and hearing loss severity. Aided sensitivity to the TFS and E cues was equally important for children with MMHL, whereas for children with NH, E cues were more important. These findings suggest that deficits in TFS perception may contribute to the variability in spoken language outcomes in children with sensorineural hearing loss.