The　purpose　of　this　paper　is　to　discuss　the　variation　of　wellbore　temperature　and　bottom-hole　pressure　with　key　factors　in　the　case　of　coupled　temperature　and　pressure　under　multi-pressure　system　during　deep-water　drilling　circulation.　According　to　the　law　of　energy　conservation　and　momentum　equation,　the　coupled　temperature　and　pressure　calculation　model　under　multi-pressure　system　is　developed　by　using　the　comprehensive　convective　heat　transfer　coefficient.　The　model　is　discretized　and　solved　by　finite　difference　method　and　Gauss　Seidel　iteration　respectively.　Then　the　calculation　results　of　this　paper　are　compared　and　verified　with　previous　research　models　and　field　measured　data.　The　results　show　that　when　the　multi-pressure　system　is　located　in　the　middle　formation,　the　temperature　of　the　annulus　corresponding　to　location　of　the　system　is　the　most　affected,　and　the　temperature　of　the　other　areas　in　annulus　is　hardly　affected.　However,　when　the　multi-pressure　system　is　located　at　the　bottom　hole,　the　annulus　temperature　is　greatly　affected　from　bottom　hole　to　mudline.　In　addition,　the　thermo-physical　parameters　of　the　drilling　fluid　can　be　changed　by　overflow　and　leakage.　When　only　overflow　occurs,　the　annulus　temperature　increases　the　most,　but　the　viscosity　decreases　the　most.　When　only　leakage　occurs,　the　annulus　temperature　decreases　the　most　and　the　viscosity　increases　the　most.　However,　when　the　overflow　rate　is　greater　than　the　leakage　rate,　the　mud　density　and　bottom-hole　pressure　increase　the　most,　and　both　increase　the　least　when　only　leakage　occurs.　Meanwhile,　bottom-hole　pressure　increases　with　the　increase　of　pump　rate　but　decreases　with　the　increase　of　inlet　temperature.　The　research　results　can　provide　theoretical　guidance　for　safe　drilling　in　complex　formations　such　as　multi-pressure　systems.