In　this　paper,　we　use　the　finite　element　method　(FEM)　to　solve　the　time-space　fractional　Bloch-Torrey　equation　on　irregular　domains　in　R-3.　Based　on　linear　Lagrange　basis　functions,　a　space　semi-discrete　FEM　scheme　is　given.　By　adopting　the　L2-1(sigma)　approximation　for　the　Caputo　fractional　derivative,　a　fully　discrete　scheme　is　presented.　Furthermore,　we　provide　the　details　on　how　to　implement　our　FEM　for　the　space　fractional　Bloch-Torrey　equation.　Also,　the　stability　and　convergence　of　the　fully　discrete　scheme　is　investigated.　The　error　estimations　with　respect　to　the　L-2　and　energy　norms　are　given.　In　addition,　some　numerical　examples　are　presented　to　verify　the　efficiency　of　our　method.　(C)　2020　Elsevier　Inc.　All　rights　reserved.