In　this　paper,　we　consider　a　modified　time　distributed-order　anomalous　sub-diffusion　equation　for　the　description　of　processes　becoming　less　anomalous　over　the　course　of　time.　First,　we　discretize　the　integral　term　using　a　mid-point　quadrature　rule　and　transform　the　time　distributed-order　fractional　diffusion　equation　into　a　multi-term　equation.　Then　applying　the　backward　difference　method　in　time　and　Galerkin　finite　element　method　in　space,　we　present　a　fully　discrete　scheme　to　solve　the　time　distributed-order　fractional　diffusion　equation.　Moreover,　the　stability　and　convergence　of　the　proposed　method　are　also　discussed.　Numerical　examples　are　given　to　verify　the　accuracy　and　stability　of　our　scheme.　(C)　2019　Elsevier　B.V.　All　rights　reserved.