The button-press task means that the subject observes a moving target and presses a button to stop it when the target enters a specified area on a computer display. Subjects perform normal task, suppressed task and delayed task. In the suppressed task, the moving target disappears at some point during the trial. In the delayed task, there is some lag time between the time of pressing button and of stopping target. In these tasks, subjects estimate the movement of the target, and press the button considering his/her own reaction time. In our previous study, we showed that cognitive and motor function was able to be evaluated by these tasks. In this study, we examined error data of children with developmental disabilities to evaluate the cognitive function, and investigated the learning processes. Moreover, we discussed the developmental stages by comparing the children with disabilities to normal control children, and we clarified the behavior characteristics of children with developmental disabilities. Asa result, it was shown that our evaluation method and system for the button-press task were effective to evaluate cognitive ability of children with developmental disabilities.