This study aimed to investigate the alterations in brain networks in patients with Alzheimer’s disease (AD) and mild cognitive impairment (MCI) based on a population-specific brain template. Previous studies on AD brain networks using graph theory rarely adopted brain templates specific for certain ethnicities. In this study, patients were divided into 3 groups: AD (n = 24), MCI (n = 27), and healthy controls (HCs, n = 33), and all of the subjects are Chinese. Functional brain networks were constructed for each group based on a Chinese brain template using resting-state functional magnetic resonance imaging (rs-fMRI) data; several graph metrics were calculated. Graph metrics with significant differences after false discovery rate (FDR) correction were analyzed with respect to correlations with four neuropsychological test scores: Mini-Mental State Examination (MMSE), Montreal Cognitive Assessment (MoCA), Activities of Daily Living (ADL), and Clinical Dementia Rating (CDR), which assessed the subjects’ cognitive functions and ability to engage in ADL. Graph metrics including assortativity coefficient, nodal degree centrality, nodal clustering coefficient, nodal efficiency, and nodal local efficiency of the frontal gyrus and cerebellum were significantly altered in AD and MCI compared with HC. Several graph metrics were significantly correlated with cognitive function and the ability to engage in daily activities. The findings suggest that altered graph metrics in the frontal gyrus may reflect brain plasticity, and that patients with MCI may have unique graph metric alterations in the cerebellum. Future graph analysis studies on functional brain networks in AD and MCI based on population-specific brain atlases for particular ethnicities may prove valuable.