Speech recognition in cochlear implant (CI) recipients is quite variable, particularly in challenging listening conditions. Demographic, audiological, and cognitive factors explain some, but not all, of this variance. The literature suggests that rapid auditory perceptual learning explains unique variance in speech recognition in listeners with normal hearing and those with hearing loss. The present study focuses on the early adaptation phase of task-specific rapid auditory perceptual learning. It investigates whether adult CI recipients exhibit this learning and, if so, whether it accounts for portions of the variance in their recognition of fast speech and speech in noise. Thirty-six adult CI recipients (ages = 35 to 77, M = 55) completed a battery of general speech recognition tests (sentences in speech-shaped noise, four-talker babble noise, and natural-fast speech), cognitive measures (vocabulary, working memory, attention, and verbal processing speed), and a rapid auditory perceptual learning task with time-compressed speech. Accuracy in the general speech recognition tasks was modeled with a series of generalized mixed models that accounted for demographic, audiological, and cognitive factors before accounting for the contribution of task-specific rapid auditory perceptual learning of time-compressed speech. Most CI recipients exhibited early task-specific rapid auditory perceptual learning of time-compressed speech within the course of the first 20 sentences. This early task-specific rapid auditory perceptual learning had unique contribution to the recognition of natural-fast speech in quiet and speech in noise, although the contribution to natural-fast speech may reflect the rapid learning that occurred in this task. When accounting for demographic and cognitive characteristics, an increase of 1 SD in the early task-specific rapid auditory perceptual learning rate was associated with ~52% increase in the odds of correctly recognizing natural-fast speech in quiet, and ~19% to 28% in the odds of correctly recognizing the different types of speech in noise. Age, vocabulary, attention, and verbal processing speed also had unique contributions to general speech recognition. However, their contribution varied between the different general speech recognition tests. Consistent with previous findings in other populations, in CI recipients, early task-specific rapid auditory perceptual, learning also accounts for some of the individual differences in the recognition of speech in noise and natural-fast speech in quiet. Thus, across populations, the early rapid adaptation phase of task-specific rapid auditory perceptual learning might serve as a skill that supports speech recognition in various adverse conditions. In CI users, the ability to rapidly adapt to ongoing acoustical challenges may be one of the factors associated with good CI outcomes. Overall, CI recipients with higher cognitive resources and faster rapid learning rates had better speech recognition.