The wildest threat for persistent operation of computing systems is the aggression of virus. The role of preventing viruses from getting further transmitted henceforth becomes more important. In this paper, the numerical solution of a computer virus model of fractional order α (0<α<1) that describes the effectiveness of antivirus has been determined by using Mahgoub Transform Iterative Method. The proposed method combines Mahgoub transform with the iterative method. The fractional order derivatives are considered in sense of Caputo. An accuracy of the obtained results reveal that the newly developed method is effective, easy to use and provides good accuracy when its results compared with Runge Kutta Method of fourth order for integer derivative.