Abstract: In this paper, we introduce a Galerkin method based on Legendre multiwavelet functions to obtain approximate solutions of a fractional model for HIV infection of CD4+T cells corresponding to a class of systems of nonlinear fractional differential equations. The method converts the model problem into a system of nonlinear algebraic equations. A numerical example is included to demonstrate the validity and applicability of the technique and the results are compared with those obtained by existing methods.