The small-world organization has been hypothesized to reflect a balance between local processing and global integration in the human brain. Previous multimodal imaging studies have consistently demonstrated that the topological architecture of the brain network is disrupted in Alzheimer's disease (AD). However, these studies have reported inconsistent results regarding the topological properties of brain alterations in AD. One potential explanation for these inconsistent results lies with the diverse homogeneity and distinct progressive stages of the AD involved in these studies, which are thought to be critical factors that might affect the results. We investigated the topological properties of brain functional networks derived from resting functional magnetic resonance imaging (fMRI) of carefully selected moderate AD patients and normal controls (NCs). Our results showed that the topological properties were found to be disrupted in AD patients, which showing increased local efficiency but decreased global efficiency. We found that the altered brain regions are mainly located in the default mode network, the temporal lobe and certain subcortical regions that are closely associated with the neuropathological changes in AD. Of note, our exploratory study revealed that the ApoE genotype modulates brain network properties, especially in AD patients.