In this paper, we propose and investigate a fractional diffusive model for hepatitis B virus (HBV) infection with capsids and immune response presented by cytotoxic T lymphocyte (CTL) cells. We derive the conditions for global asymptotic stability of the steady states of the model in terms of the basic reproduction numberR0and the immune response reproduction numberR1. By constructing appropriate Lyapunov functionals, it is shown that the infection-free equilibrium is globally asymptotically stable whenR0≤ 1, the immune-free infection equilibrium is globally asymptotically stable whenR1≤ 1 <R0and the infection equilibrium with CTL immune response is globally asymptotically stable whenR1> 1. Numerical simulations are performed to illustrate the analytical results.