As　the　most　adequate　configuration,　steel　lazy　wave　risers　(SLWRs)　are　developed　for　deep-sea　oil　and　gas　exploitation　projects.　However,　SLWRs　are　very　sensitive　to　ocean　currents　and　internal　solitary　wave　(ISW).　Based　on　a　3D　modified　slender　rod　theory,　a　nonlinear　dynamic　model　for　the　SLWR　suffering　from　vessel　motions　(VMs),　surface　waves　(SWs),　ocean　currents　and　ISW　is　established.　According　to　the　equivalence　principle,　equivalent　parameters　for　the　buoyancy　section　are　introduced　in　the　dynamic　model.　Besides,　the　applicability　and　formulas　for　different　ISW　theories　are　described.　Finally,　the　nonlinear　SLWR　dynamic　responses　under　four　cases　are　compared　to　investigate　the　influence　of　the　ISW　and　ocean　currents.　The　results　show　that　the　ISW　can　significantly　induce　the　oscillation　displacements　of　the　SLWR,　especially　along　the　horizontal　direction　near　the　ISW　interface.　The　dynamic　bending　moments　between　the　hang-off　point　and　interface　significantly　intensify　due　to　the　ISW.　The　ISW　affects　the　dynamic　effective　tension　of　the　SLWR　in　the　lower　layer　fluid　more　markedly　than　that　in　the　upper　layer　fluid.　In　addition　to　the　interface　zone,　the　impact　of　ocean　currents　on　the　SLWR　dynamic　response　seems　to　be　more　significant　than　that　of　the　ISW.