Previous　front-tracking　(FT)　method-based　models　to　simulate　droplet　motion　on　a　solid　surface　with　a　moving　contact　line　(MCL)　are　limited　to　two-dimensional　models　in　which　the　Navier　boundary　condition　(NBC)　is　employed　for　the　MCL.　In　this　paper,　we　develop　a　three-dimensional　FT　method　that　integrates　the　generalized　Navier　boundary　condition　(GNBC)　to　model　the　MCL.　This　GNBC-based　FT　method　addresses　several　key　issues,　such　as　the　integration　of　GNBC　for　the　dynamic　description　of　the　MCL　and　its　coupling　with　the　surrounding　flow,　the　accurate　updating　of　the　density　and　viscosity　of　the　two-phase　fluid　near　the　contact　line,　and　the　restructuring　of　the　Lagrangian　mesh　for　tracking　the　drop　surface,　especially　near　the　contact　line.　The　stability　and　accuracy　of　the　present　numerical　method　are　validated　by　several　tests:　(1)　numerical　performance　tests,　(2)　simulation　of　the　transient　and　steady-state　shapes　of　droplets　under　flow　with　a　fixed　contact　line,　and　(3)　simulation　of　a　droplet　spreading　under　gravity　and　moving　under　a　shear　flow　with　MCLs.　Excellent　agreement　is　achieved　between　the　results　obtained　by　our　model　and　the　data　obtained　by　other　theoretical　and　numerical　approaches.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.