In　this　paper,　the　numerical　analysis　for　a　multi-term　time　fracstional　and　Riesz　space　distributed-order　wave　equation　is　discussed　on　an　irregular　convex　domain.　Firstly,　the　equation　is　transformed　into　a　multi-term　time-space　fractional　wave　equation　using　the　mid-point　quadrature　rule　to　approximate　the　distributed-order　Riesz　space　derivative.　Next,　the　equation　is　solved　by　discretising　in　time　using　a　Crank–Nicolson　scheme　and　in　space　using　the　finite　element　method　(FEM)with　an　unstructured　mesh,　respectively.　Furthermore,　stability　and　convergence　are　investigated　by　introducing　some　important　lemmas　on　irregular　convex　domain.　Finally,　some　examples　are　provided　to　show　the　effectiveness　and　correctness　of　the　proposed　numerical　method.　©　2019　Elsevier　Inc.