The　time–space　fractional　Bloch–Torrey　equation　(TS-FBTE)　has　been　proposed　to　simulate　anomalous　diffusion　in　the　human　brain.　However,　the　development　of　numerical　methods　and　theoretical　analysis　for　multi-term　time–space　fractional　Bloch–Torrey　equations　in　three　dimensions　is　still　limited.　In　this　paper,　we　consider　a　class　of　3-D　multi-term　time–space　fractional　Bloch–Torrey　equations　(3D-MTTS-FBTEs).　Firstly,　we　adopt　a　fractional　centred　difference　scheme　to　discretize　the　Riesz　fractional　derivative　and　propose　a　fractional　alternating-direction　implicit　method　(FADIM)　for　the　model.　Secondly,　the　solvability,　stability　and　convergence　of　the　method　are　investigated.　Finally,　numerical　results　are　presented　to　support　our　theoretical　analysis.　In　addition,　to　demonstrate　the　applicability　of　our　method,　we　consider　a　coupled　3-D　FBTE　as　an　example　to　solve　and　exhibit　the　effects　on　the　behaviour　of　the　transverse　magnetization.　©　2018　Elsevier　Ltd