The human brain undergoes complex reorganization and changes during aging. Using graph theory, scientists can find differences in topological properties of functional brain networks between young and elderly adults. However, these differences are sometimes significant and sometimes not. Several studies have even identified disparate differences in topological properties during normal aging or in age-related diseases. One possible reason for this issue is that existing brain network construction methods cannot fully extract the "intrinsic edges" to prevent useful signals from being buried into noises. This paper proposes a new subnetwork voting (SNV) method with sliding window to construct functional brain networks for young and elderly adults. Differences in the topological properties of brain networks constructed from the classic and SNV methods were consistent. Statistical analysis showed that the SNV method can identify much more statistically significant differences between groups than the classic method. Moreover, support vector machine was utilized to classify young and elderly adults; its accuracy, based on the SNV method, reached 89.3%, significantly higher than that with classic method. Therefore, the SNV method can improve consistency within a group and highlight differences between groups, which can be valuable for the exploration and auxiliary diagnosis of aging and age-related diseases.