Not all of the variance in speech-recognition performance of cochlear implant (CI) users can be explained by biographic and auditory factors. In normal-hearing listeners, linguistic and cognitive factors determine most of speech-in-noise performance. The current study explored specifically the influence of visually measured lexical-access ability compared with other cognitive factors on speech recognition of 24 postlingually deafened CI users. Speech-recognition performance was measured with monosyllables in quiet (consonant-vowel-consonant [CVC]), sentences-in-noise (SIN), and digit-triplets in noise (DIN). In addition to a composite variable of lexical-access ability (LA), measured with a lexical-decision test (LDT) and word-naming task, vocabulary size, working-memory capacity (Reading Span test [RSpan]), and a visual analogue of the SIN test (text reception threshold test) were measured. The DIN test was used to correct for auditory factors in SIN thresholds by taking the difference between SIN and DIN: SRTdiff. Correlation analyses revealed that duration of hearing loss (dHL) was related to SIN thresholds. Better working-memory capacity was related to SIN and SRTdiff scores. LDT reaction time was positively correlated with SRTdiff scores. No significant relationships were found for CVC or DIN scores with the predictor variables. Regression analyses showed that together with dHL, RSpan explained 55% of the variance in SIN thresholds. When controlling for auditory performance, LA, LDT, and RSpan separately explained, together with dHL, respectively 37%, 36%, and 46% of the variance in SRTdiff outcome. The results suggest that poor verbal working-memory capacity and to a lesser extent poor lexical-access ability limit speech-recognition ability in listeners with a CI.