Although a number of cognitive deficits have been described in individuals with intellectual disabilities (ID), few studies have examined the use of computer-assisted cognitive training programmes in this group of people. This study sought to determine the cognitive mechanisms underlying 16 activities included in Armoni, a computerized cognitive training programme for individuals with ID, in order to validate its use with this population. Fifty adults with ID from four residential care centres in Spain underwent neuropsychological testing tapping attention, verbal memory, visual memory, comprehension, visuoperception, visuoconstruction, naming ability, verbal fluency, verbal reasoning and motor function. In addition, they performed 16 activities included in the Armoni programme. The relationships between cognitive function and the computer-based activities were assessed using Spearman correlations. Stepwise multiple regression analyses were then used to explore how cognitive function predicted the performance of individuals with ID on the programme activities. Most programme activities correlated with visuoconstruction, comprehension and naming ability. Naming ability, visual memory, comprehension and visuoconstruction contributed the most to the predictive models regarding performance on the Armoni activities. Our findings support the validity of Armoni for cognitive training in individuals with ID.