In this article, we present a fractional order HIV-1 infection model of CD4+ T-cell. We analyze the effect of the changing the average number of the viral particle N with initial conditions of the presented model. The Laplace Adomian decomposition method is applying to check the analytical solution of the problem. We obtain the solutions of the fractional order HIV-1 model in the form of infinite series. The concerned series rapidly converges to its exact value. Moreover, we compare our results with the results obtained by Runge-Kutta method in case of integer order derivative.