A new resident virus propagation model with graded infection rate is established based on the properties of two important stages undergoing by resident virus, which are the latent phase, in which resident virus cannot infect other hosts because it has not yet been loaded into memory and the active phase, in which resident virus resides in memory and infects any suitable program that is executed on the computer. Two computer compartments with different infection rate are established. Furthermore, the dynamic behaviors of this model are investigated by stability theory and numerical simulations. It is found that the dynamical properties of this model are determined by basic reproductive rate. Specifically, virus-free equilibrium is globally asymptotically stable if basic reproductive rate is less than or equal to one , whereas the local asymptotical stability of the viral equilibrium is guaranteed if basic reproductive rate is bigger than one, followed by a conjecture on its global stability. Then the sensitivity analysis of basic reproductive rate to the system parameters is investigated and a collection of policies is advised to control the spread of computer virus over the Internet.