Down's syndrome is a chromosomal disorder that invariably results in both intellectual disability and Alzheimer's disease neuropathology. However, only a limited number of studies to date have investigated intrinsic brain network organisation in people with Down's syndrome, none of which addressed the links between functional connectivity and Alzheimer's disease. In this cross-sectional study, we employed 11 C-Pittsburgh Compound-B (PiB) positron emission tomography in order to group participants with Down's syndrome based on the presence of fibrillar beta-amyloid neuropathology. We also acquired resting state functional magnetic resonance imaging data to interrogate the connectivity of the default mode network; a large-scale system with demonstrated links to Alzheimer's disease. The results revealed widespread positive connectivity of the default mode network in people with Down's syndrome (n = 34, ages 30-55, median age = 43.5) and a stark lack of anti-correlation. However, in contrast to typically developing controls (n = 20, ages 30-55, median age = 43.5), the Down's syndrome group also showed significantly weaker connections in localised frontal and posterior brain regions. Notably, while a comparison of the PiB-negative Down's syndrome group (n = 19, ages 30-48, median age = 41.0) to controls suggested that alterations in default mode connectivity to frontal brain regions are related to atypical development, a comparison of the PiB-positive (n = 15, ages 39-55, median age = 48.0) and PiB-negative Down's syndrome groups indicated that aberrant connectivity in posterior cortices is associated with the presence of Alzheimer's disease neuropathology. Such distinct profiles of altered connectivity not only further our understanding of the brain physiology that underlies these two inherently linked conditions but may also potentially provide a biomarker for future studies of neurodegeneration in people with Down's syndrome.