To provide technical support for computer diagnosis of Alzheimer's disease (AD) patients, the data of resting-state functional magnetic resonance imaging (fMRI) are collected from 9 AD patients and 11 normal elderly people.We adopt the Automated Anatomical Labeling (AAL) template to divide the brain into 90 regions.The corresponding time series of each region are calculated and the values in the correlation matrix after mathematics transformation are taken as the weights of edges between the brain regions.Then we build the weighted brain network of each subject.Based on the above, we study the characteristics of the brain network in the specific brain regions of AD patients and normal elderly group respectively.The simulation results show that compared with the normal elderly group, the network efficiency of the weighted brain network in patients with AD decreased, and the characteristic path lengths are longer than those of the normal group under different Sparsity thresholds.This result can provide a theoretical basis for early diagnosis of AD patients.