The　generalized　finite　difference　method　(GFDM)　is　a　newly-developed　domain-type　meshless　method,　which　could　truly　get　rid　of　time-consuming　meshing　generation　and　numerical　quadrature　at　every　time　step　and　be　adopted　to　simulate　the　non-linear　moving-boundary　physical　problems.　According　to　the　Lagrangian　approach,　the　GFDM　and　the　leap-frog　approach　were　adopted　for　spatial　and　temporal　discretizations　of　the　sloshing　problem　in　a　two-dimensional　numerical　tank,　respectively.　Results　and　comparisons　via　the　numerical　examples　of　free　sloshing　and　forced　sloshing　verified　the　accuracy,　efficiency　and　stability　of　the　proposed　meshless　numerical　scheme.　©　2016,　Editorial　Department　of　Journal　of　Sichuan　University　(Engineering　Science　Edition).　All　right　reserved.