According to the characteristics and propagation law of zero-day virus, the propagation model and stability of zero-day virus are studied. Firstly, the mechanism of zero-day virus transmission is analyzed. Based on the Susceptible-Infected-Removed-Susceptible(SIRS) virus transmission model, the node of infection state is redefined, the node of execution state and the node of damage state are introduced, and the zero-day virus transmission Susceptible - Initial-state-of infection- Zero-day - Damaged - Recovery (SIZDR) dynamic model is established. Secondly, the local stability of the system equilibrium point, the basic regeneration number and its influence on the scale of virus transmission are analyzed by using Rous stability criterion. Finally, the local stability of the model is verified by simulation, and the influence of node infection rate, node degree and node damage rate on zero-day virus transmission is analyzed. Theoretical analysis and simulation results show that the proposed model can objectively reflect the law of zero-day virus transmission, and the magnitude of zero-day virus spread is positively correlated with node degree and node infection rate, and negatively correlated with node damage rate. Targeted prevention and control of known viruses can effectively improve the defense effect against zero-day viruses.