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In this paper, by considering the development of antivirus software always lags behind the emergence of new virus and the point-to-group information propagation mode, a new computer virus model with point to group and discontinuous anti-virus strategy is presented. To the best of our knowledge, this is the first computer virus model that takes into account the effect of discontinuous anti-virus strategy. The dynamic properties of this model are investigated comprehensively. Specifically, it is found that in the case that the equilibrium is asymptotically stable, the convergence to the equilibrium can actually be achieved in finite time, and the time can be estimated in terms of the model parameters, the initial number of the uninfected computer and latent computer and the initial anti-virus strength, which means the virus in the network can be controlled or eliminated in finite time by increasing the anti-virus strength. Finally, two illustrative examples are also given to support the theoretical results. [ABSTRACT FROM AUTHOR]