In　this　paper,　the　unstructured　mesh　Galerkin　finite　element　method　with　a　weighted　and　shifted　Grünwald　difference　approximation　and　Composite　Trapezoid　formula　is　presented　to　solve　the　nonhomogeneous　two-dimensional　distributed　order　time　fractional　Cable　equation　on　irregular　convex　domains.　The　Crank–Nicolson　type　discretization　of　the　finite　element　scheme　is　implemented　to　obtain　the　numerical　solution.　The　stability　and　convergence　of　the　numerical　scheme　are　discussed　and　derived.　Finally,　some　numerical　examples　on　irregular　convex　domains　are　given　to　confirm　our　theoretical　results.　©　2020　Elsevier　Ltd