The purpose of this study is to explore the changes in functional brain networks of AD patients using complex network theory. In this study, resting-state fMRI datasets of 10 AD patients and 11 healthy controls were collected. Time series of 90 brain regions were extracted from the fMRI datasets after preprocessing. Pearson correlation method was used to calculate the correlation coefficient between any two time series. Then, a wide threshold range was selected to transform the adjacency matrix to a binary matrix under a different threshold. The topology parameters of each binary network were calculated, and all of them were then averaged within a group. During the evolution, node betweenness and the Euclidean distance between the nodes were set as control factors. Each binary network of healthy controls underwent evolution of 100 steps in accordance with the evolution rules. Then, the topology parameters of the evolution network were calculated. Finally, support vector machine (SVM) was used to classify the network topology parameters of the evolution network and to determine whether evolution results matched the datasets from AD patients. We found there were differing degrees of decline in global efficiency, clustering coefficient, number of edges and transitivity in AD patients compared with healthy controls. The topology parameters of the evolution network tended toward those of the AD group. The results of SVM classification of the evolution network show that the evolution network had a greater probability to be classified as an AD patients group. A new biological marker for diagnosis of AD was provided through comparison of topology parameters between AD patients and healthy controls. The study of network evolution strategies enriched the method of brain network evolution. The use of SVM to classify the results of network evolution provides an objective criteria for determining evolution results.