Although Down syndrome (DS) is the most common genetic cause of neurodevelopmental delay, few neuroimaging studies have explored this population. This investigation aimed to study whole-brain resting-state spontaneous brain activity using fractional amplitude of low-frequency fluctuation (fALFF) and regional homogeneity (ReHo) strategies to find differences in spontaneous brain activity among young people with DS and controls and to correlate these results with cognitive outcomes. The sample comprised 18 persons with DS (age mean = 28.67, standard deviation = 4.18) and 18 controls (age mean = 28.56, standard deviation = 4.26). fALFF and ReHo analyses were performed, and the results were correlated with other cognitive variables also collected (KBIT-2 and verbal fluency test). Increased activity was found in DS using fALFF in areas involving the frontal and temporal lobes and left cerebellum anterior lobe. Decreased activity in DS was found in the left parietal and occipital lobe, the left limbic lobe and the left cerebellum posterior lobe. ReHo analysis showed increased activity in certain DS areas of the left frontal lobe and left rectus, as well as the inferior temporal lobe. The areas with decreased activity in the DS participants were regions of the frontal lobe and the right limbic lobe. Altered fALFF and ReHo were found in the DS population, and this alteration could predict the cognitive abilities of the participants. To our knowledge, this is the first study to explore regional spontaneous brain activity in a population with DS. Moreover, this study suggests the possibility of using fALFF and ReHo as biomarkers of cognitive function, which is highly important given the difficulties in cognitively evaluating this population to assess dementia. More research is needed, however, to demonstrate its utility.