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.　©　2019　Elsevier　B.V.