Older adults may harbor large amounts of amyloid-β (Aβ) pathology, yet still perform at age-normal levels on memory assessments. We tested whether functional brain networks confer resilience or compensatory mechanisms to support memory in the face of Aβ pathology. Sixty-five cognitively normal older adults received high-resolution resting state fMRI to assess functional networks, 18F-florbetapir-PET to measure Aβ, and a memory assessment. We characterized functional networks with graph metrics of local efficiency (information transfer), modularity (specialization of functional modules), and small worldness (balance of integration and segregation). There was no difference in functional network measures between older adults with high Aβ (Aβ+) compared to those with no/low Aβ (Aβ-). However, in Aβ+ older adults, increased local efficiency, modularity, and small worldness were associated with better memory performance, while this relationship did not occur Aβ- older adults. Further, the association between increased local efficiency and better memory performance in Aβ+ older adults was localized to local efficiency of the default mode network and hippocampus, regions vulnerable to Aβ and involved in memory processing. Our results suggest functional networks with modular and efficient structures are associated with resilience to Aβ pathology, providing a functional target for intervention.