In　this　paper,　we　propose　a　second-order　operator　splitting　spectral　element　method　for　solving　fractional　reaction-diffusion　equations.　In　order　to　achieve　a　fast　second-order　scheme　in　time,　we　decompose　the　original　equation　into　linear　and　nonlinear　sub-equations,　and　combine　a　quarter-time　nonlinear　solver　and　a　half-time　linear　solver　followed　by　final　quarter-time　nonlinear　solver.　The　spatial　discretization　is　eigen-decomposition　based　on　spectral　element　method.　Since　this　method　gives　a　full　diagonal　representation　of　the　fractional　operator　and　gets　an　exponential　convergence　in　space.　We　have　an　accurate　and　efficient　approach　for　solving　spacial　fractional　reaction-diffusion　equations.　Some　numerical　experiments　are　carried　out　to　demonstrate　the　accuracy　and　efficiency　of　this　method.　Finally,　we　apply　the　proposed　method　to　investigate　the　effect　of　the　fractional　order　in　the　fractional　reaction-diffusion　equations.　©　The　Author(s)　2020.