The study of cognitive activity in Down syndrome (DS) is relevant because of the inherent intellectual disability (ID). The aim of this research is to estimate network complexity indicators in 24 regions belonging to the Default Mode Network (DMN) through fMRI signal with a resting state paradigm in DS. In addition, we intend to study their possible relationship with adapted neuropsychological test scores to assess IQ and cognitive performance. The sample was composed of 35 people with DS between the ages of 16 and 35. However, due to excessive movement, 13 of the 35 subjects were not considered, so our final sample was composed of 22 (M = 25.55 and SD = 5.12). T1 imaging and BOLD signal were acquired with a 3-Tesla scanner and participants were assessed with the Kaufman Brief Intelligence Test (KBIT) and the Frontal Assessment Battery (FAB). Participants’ mental age was calculated using a heuristic of KBIT neuropsychological scores. High variability in DMN complexity indicators has been found through individuals. Similarly, high variability was found in the neuropsychological assessment, probably because of the heterogeneity within the individuals of study. Therefore, both issues complicate the estimation of the parameters by conventional statistical regression models and we propose the use of more robust inferential statistical tools as a method to assess the relationship between complexity and neuropsychological indicators. Our finding is that there is an enormous difficulty in finding the usual structure in SD DMN and the complexity structure of functional connectivity networks is inversely related to cognitive performance.