Elderly listeners are known to differ considerably in their ability to understand speech in noise. Several studies have addressed the underlying factors that contribute to these differences. These factors include audibility, and age-related changes in supra-threshold auditory processing abilities, and it has been suggested that differences in cognitive abilities may also be important. The objective of this study was to investigate associations between performance in cognitive tasks and speech recognition under different listening conditions in older adults with either age appropriate hearing or hearing-impairment. To that end, speech recognition threshold (SRT) measurements were performed under several masking conditions that varied along the perceptual dimensions of dip listening, spatial separation, and informational masking. In addition, a neuropsychological test battery was administered, which included measures of verbal working and short-term memory, executive functioning, selective and divided attention, and lexical and semantic abilities. Age-matched groups of older adults with either age-appropriate hearing (ENH, n = 20) or aided hearing impairment (EHI, n = 21) participated. In repeated linear regression analyses, composite scores of cognitive test outcomes (evaluated using PCA) were included to predict SRTs. These associations were different for the two groups. When hearing thresholds were controlled for, composed cognitive factors were significantly associated with the SRTs for the ENH listeners. Whereas better lexical and semantic abilities were associated with lower (better) SRTs in this group, there was a negative association between attentional abilities and speech recognition in the presence of spatially separated speech-like maskers. For the EHI group, the pure-tone thresholds (averaged across 0.5, 1, 2, and 4 kHz) were significantly associated with the SRTs, despite the fact that all signals were amplified and therefore in principle audible.