Abstract: According to the case of node increasing and decreasing, the network virus spreading model and its stability are researched. Considering the increasing and decreasing of network nodes, the network virus spreading model is constructed based on the mechanism of node increasing and decreasing. And then the stability of the presented model, basic reproductive number R₀, and the influence of virus spreading stability are analyzed via Routh-Hurwitz stability criterion. Finally, the effects of three parameters on the process of virus transmission are studied by changing the number of nodes and the removal rate of susceptible and infected nodes. Simulations are demonstrated that network virus spreading can be controlled by effective adjusting the number of network nodes.