Recently, much focus has been given to find reliable and more effective approximations for solving fuzzy fractional differential equations that describe biological mathematical models. The fourth order Runge-Kutta method based on Centroidal mean is the approximate method used for solving linear and nonlinear differential equations. Here, the Fuzzy Fractional Fourth Order Runge-Kutta Method based on Centroidal Mean (FFRK4CeM) is studied to provide approximate solution for the system of Fuzzy Fractional Differential Equation (FFDE) and comparing the result with the well-known Fuzzy Fractional Fourth Order Runge-Kutta method (FFRK4). This study is used to describe HIV infection in the form of fuzzy fractional differential equations and FFRK4CeM is applied to solve these equations. The key benefit of this approach is that no parametric assumptions are required for the problem. This method can be applied to weak and strong nonlinear issues. Unlike existing analytical approximate methods, the recommended method produces solutions without perturbation, linearization, or discretization. The numerical results of the model indicate that this method is effective and easy to use in FFDE systems.