The　time-dependent　mild-slope　equation　(MSE)　is　a　second-order　hyperbolic　equation,　which　is　adopted　to　consider　the　irregularity　of　waves.　For　the　difficulty　of　directly　solving　the　partial　derivative　terms　and　the　second-order　time　derivative　term,　a　novel　mesh-free　numerical　scheme,　based　on　the　generalized　finite　difference　method　(GFDM)　and　the　Houbolt　finite　difference　method　(HFDM),　is　developed　to　promote　the　precision　and　efficiency　of　the　solution　to　time-dependent　MSE.　Based　on　the　local　characteristics　of　the　GFDM,　as　a　new　domain-type　meshless　method,　the　linear　combinations　of　nearby　function　values　can　be　straightforwardly　and　efficiently　implemented　to　compute　the　partial　derivative　term.　It　is　worth　noting　that　the　application　of　the　HFDM,　an　unconditionally　stable　finite　difference　time　marching　scheme,　to　solve　the　second-order　time　derivative　term　is　critical.　The　results　obtained　from　four　examples　show　that　the　propagation　of　waves　can　be　successfully　simulated　by　the　proposed　numerical　scheme　in　complex　seabed　terrain.　In　addition,　the　energy　conversion　of　waves　in　long-distance　wave　propagation　can　be　accurately　captured　using　fast　Fourier　transform　(FFT)　analysis,　which　investigates　the　energy　conservation　in　wave　shoaling　problems.