Functional brain connectivity is altered during the pathological processes of Alzheimer's disease (AD), but the specific evolutional rules are insufficiently understood. Resting-state functional magnetic resonance imaging indicates that the functional brain networks of individuals with AD tend to be disrupted in hub-like nodes, shifting from a small world architecture to a random profile. Here, we proposed a novel evolution model based on computational experiments to simulate the transition of functional brain networks from normal to AD. Specifically, we simulated the rearrangement of edges in a pathological process by a high probability of disconnecting edges between hub-like nodes, and by generating edges between random pair of nodes. Subsequently, four topological properties and a nodal distribution were used to evaluate our model. Compared with random evolution as a null model, our model captured well the topological alteration of functional brain networks during the pathological process. Moreover, we implemented two kinds of network attack to imitate the damage incurred by the brain in AD. Topological changes were better explained by 'hub attacks' than by 'random attacks', indicating the fragility of hubs in individuals with AD. This model clarifies the disruption of functional brain networks in AD, providing a new perspective on topological alterations.