In　this　paper　we　propose　a　stable　finite　difference　method　to　solve　the　fractional　reaction-diffusion　systems　in　a　two-dimensional　domain.　The　space　discretization　is　implemented　by　the　weighted　shifted　Grunwald　difference　(WSGD)　which　results　in　a　stiff　system　of　nonlinear　ordinary　differential　equations　(ODEs).　This　system　of　ordinary　differential　equations　is　solved　by　an　efficient　compact　implicit　integration　factor　(cIIF)　method.　The　stability　of　the　second　order　cIIF　scheme　is　proved　in　the　discrete　L-2-norm.　We　also　prove　the　second-order　convergence　of　the　proposed　scheme.　Numerical　examples　are　given　to　demonstrate　the　accuracy,　efficiency,　and　robustness　of　the　method.