In　this　paper,　a　numerical　wave　flume　is　formed　by　combining　the　generalized　finite　difference　method　(GFDM),　the　Runge–Kutta　method,　the　semi-Lagrangian　technique,　the　ramping　function　and　the　sponge　layer　to　efficiently　and　accurately　analyze　the　propagation　of　nonlinear　water　waves.　On　the　basis　of　potential　flow,　the　mathematical　description　of　wave　propagation　is　a　time-dependent　boundary　value　problem,　governed　by　a　Laplace　equation　for　velocity　potential　and　two　nonlinear　free-surface　boundary　conditions.　The　incident　waves　are　introduced　by　imposing　horizontal　velocity　along　upstream　boundary,　as　a　sponge　layer　is　placed　at　the　end　of　flume　to　absorb　wave　energy　and　avoid　any　reflection　of　waves.　The　GFDM,　a　newly-developed　meshless　numerical　method,　and　the　second-order　Runge–Kutta　method　were,　respectively,　adopted　for　spatial　and　temporal　discretizations　of　the　moving-boundary　problems.　The　GFDM,　which　is　truly　free　from　mesh　generation　and　numerical　quadrature,　is　easy-to-program,　straightforward　and　efficient,　especially　for　moving-boundary　problems.　Four　numerical　examples　are　adopted　in　this　paper　to　validate　the　stability,　the　efficiency　and　the　accuracy　of　the　proposed　meshless　numerical　wave　flume.　The　GFDM　results　were　compared　with　other　numerical　solutions　and　experimental　data　to　verify　the　merits　and　robustness　of　the　proposed　meshless　numerical　model.　©　2016　Elsevier　Ltd