According to the spreading characteristic of new escape virus, a novel network virus spreading model and its stability were researched under the escape mechanism to provide a theoretical reference for defenders. Firstly, three transformation modes were derived based on the exposed characteristic of new network virus from the exposed nodes, and then a novel network virus spreading model was constructed under the exposed mechanism. Secondly, by using Routh stability criterion, the stability of system equilibrium point was demonstrated and the basic reproductive number R₀was calculated. Finally, simulations were demonstrated for the influence of three transfer parameters on system stability. Theoretical research and simulations showed that if the basic reproductive number R₀≤1, the disease-free equilibrium was locally asymptotically stable; if R₀>1, the endemic equilibrium was locally asymptotically stable. By adjusting the probability of three kinds of metastasis in the escape state, the basic reproductive number of the system could be reduced, and the network was maintained in a disease-free healthy state. The network could be controlled in the disease-free equilibrium by increasing transition probability θfrom escape state to susceptible state, bfrom escape state to removed state, or decreasing γ from escape state to infected state, so as to maintain network security.