In　this　work,　a　phase-field-based　multiple-relaxation-time　lattice　Boltzmann　(LB)　model　is　developed　to　simulate　three-dimensional　(3D)　multiphase　flows　with　moderate　density　ratio.　Inspired　by　the　work　of　Liang　et　al.　[H.　Liang,　B.　C.　Shi,　Z.　L.　Guo,　Z.　H.　Chai,　Phase-field-based　multiple-relaxation-time　lattice　Boltz　Mann　model　for　incompressible　multiphase　flows,　Phys.　Rev.　E,　89(2014)　053320.],　a　time-dependent　source　term　is　added　in　the　LB　equation　for　interface　so　that　the　3D　Cahn-Hilliard　equation　can　be　recovered　precisely.　The　Navier-Stokes　equations　are　solved　by　introducing　a　pressure　distribution　function,　which　helps　reduce　the　discretization　errors　in　calculation　of　density　gradient　thereby　improving　the　numerical　stability　for　variable　density.　An　interfacial　force　of　potential　form　is　utilized　to　effectively　suppress　spurious　velocities　at　the　interface　and　is　incorporated　into　the　LB　equation　as　an　additional　body　force.　The　present　3D　model　is　tested　by　several　classic　numerical　examples　including　the　solid　body　rotation,　the　stationary　droplet　test,　the　droplet　deformation　and　breakup　in　a　simple　shear　flow　and　the　Rayleigh-Taylor　instability.　Simulation　results　are　shown　to　be　in　good　agreement　with　theoretical　predictions,　available　experimental　or　numerical　data,　demonstrating　a　good　capability　of　the　present　model　in　capturing　the　interface,　dealing　with　topological　changes,　and　simulating　variable　density　ratio.　In　addition,　it　is　interestingly　found　that　the　Rayleigh-Taylor　instability　will　be　totally　suppressed　when　the　Weber　number　does　not　exceed　a　critical　value.　(C)　2016　Elsevier　B.V.　All　rights　reserved.