In the research of the fMRI based brain functional network, the pairwise correlation between vertices usually means the similarity between BOLD signals. Our analysis found that the low (0:01-0:06 Hz), intermediate (0:06-0:15 Hz), and high (0:15-0:2 Hz) bands of the BOLD signal are not synchronous. Therefore, this paper presents a voxelwise based multi-frequency band brain functional network model, called Multi-graph brain functional network. First, our analysis found the low-frequency information on the BOLD signal of the brain functional network obscures the other information because of its high intensity. Then, a low-, intermediate-, and high-band brain functional networks were constructed by dividing the BOLD signals. After that, using complex network analysis, we found that different frequency bands have different properties; the modulation in low-frequency is higher than that of the intermediate and high frequency. The power distributions of different frequency bands were also significantly different, and the 'hub' vertices under all frequency bands are evenly distributed. Compared to a full-frequency network, the multi-graph model enhances the accuracy of the classification of Alzheimer's disease.