A lattice Boltzmann method(LBM) for two-dimensional fractional reaction-diffusion equations involving Riemann-Liouville derivatives is proposed. Firstly, fractional integral terms in equations are discretized. Then, with Chapman-Enskog analysis and Taylor-expansion technology two-dimensional fractional reaction-diffusion equations are recovered from the LB model. Equilibrium state of distribution function in each velocity direction is derived. Finally, the LB model is tested with numerical examples. It was found that numerical results agree well with analytical solutions.