In　magnetic　resonance　imaging　of　the　human　brain,　the　diffusion　process　of　tissue　water　is　considered　in　the　complex　tissue　environment　of　cells,　membranes　and　connective　tissue.　Models　based　on　fractional　order　Bloch-Torrey　equations　are　known　to　provide　insights　into　tissue　structures　and　the　microenvironment.　In　this　paper,　we　consider　new　two-dimensional　multi-term　time　and　space　fractional　Bloch-Torrey　equations　with　variable　coefficients　on　irregular　convex　domains,　which　involve　the　Caputo　time　fractional　derivative　and　the　Riemann-Liouville　space　fractional　derivative.　An　unstructured-mesh　Galerkin　finite　element　method　is　used　to　discretize　the　spatial　fractional　derivative,　while　for　each　time　fractional　derivative　we　use　the　L1　scheme　on　a　temporal　graded　mesh.　The　stability　and　convergence　of　the　fully　discrete　scheme　are　proved.　Numerical　examples　are　given　to　verify　the　efficiency　of　our　method.　(C)　2020　Elsevier　Ltd.　All　rights　reserved.