Fractional differential equations play an important role in modeling problems in physics and engineering such as polymer physics, viscoelastic materials, viscous damp ing and seismic analysis. In this project, we are interested in the numerical resolution of a time-fractional diffusion equation, which is obtained from the classical diffusion equation by replacing the first-order time derivative with a fractional derivative. Our main purpose is to study the Ll-scheme which is one of the most successful numerical schemes, combined with a Galerkin finite element method in space. We investigate the stability and convergence of the scheme and present a rigorous error analysis. Numerical tests will be presented to confirm the theoretical results.