In this article, we present a fractional order HIV-1 infectionmodel of CD4+ T-cell. We analyze the effect of the changing the averagenumber of the viral particle N with initial conditions of the presentedmodel. The Laplace Adomian decomposition method is applying to checkthe analytical solution of the problem. We obtain the solutions of thefractional order HIV-1 model in the form of infinite series. The concernedseries rapidly converges to its exact value. Moreover, we compare ourresults with the results obtained by Runge-Kutta method in case of integerorder derivative.