Introduction Despite the developing technology of cochlear implants (CIs), implanted prelingual hearing-impaired children exhibit variable speech processing outcomes. When these children match in personal and implant-related criteria, the CI outcome variability could be related to higher-order cognitive impairment. Objectives To evaluate different domains of cognitive function in good versus poor CI performers using a multidisciplinary approach and to find the relationship between these functions and different levels of speech processing. Methods This observational, cross-sectional study used the word recognition score (WRS) test to categorize 40 children with CIs into 20 good (WRS/65%) and 20 poor performers (WRS < 65%). All participants were examined for speech processing at different levels (auditory processing and spoken language) and cognitive functioning using (1) verbal tests (verbal component of Stanford-Binet intelligence [SBIS], auditory memory, auditory vigilance, and P300); and (2) performance tasks (performance components of SBIS, and trail making test). Results The outcomes of speech processing at different functional levels and both domains of cognitive function were analyzed and correlated. Speech processing was impaired significantly in poor CI performers. This group also showed a significant cognitive function deficit, in which the verbal abilities were more affected (in 93.5%) than in the good performers (in 69.5%). Moreover, cognitive function revealed a significant correlation and predictive effect on the CI speech outcomes. Conclusion Cognitive function impairment represented an important factor that underlies the variable speech proficiency in cochlear-implanted children. A multidisciplinary evaluation of cognitive function would provide a comprehensive overview to improve training strategies.