The　mild　slope　equation　(MSE)　has　been　widely　used　to　describe　combined　wave　refraction　and　diffraction　in　the　field　of　coastal　and　offshore　engineering　owing　to　its　applicability　for　a　wide　range　of　wave　frequencies.　In　this　paper,　a　meshless　numerical　algorithm,　based　on　the　generalized　finite　difference　method　(GFDM),　is　firstly　proposed　to　efficiently　and　accurately　solve　the　MSE.　As　a　newly-developed　domain-type　meshless　method,　the　GFDM　can　truly　get　rid　of　time-consuming　meshing　generation　and　numerical　quadrature.　The　partial　differential　terms　of　the　MSE　for　each　point　in　the　computational　domain　can　be　discretized　into　linear　combinations　of　nearby　function　values　with　the　moving-least-squares　method　of　the　GFDM,　so　the　numerical　implementation　is　very　convenient　and　efficient.　To　evaluate　the　accuracy　and　capability　of　the　proposed　scheme　for　MSE,　a　series　of　numerical　tests　were　conducted,　covering　a　range　of　complexity　that　included　propagation　and　transformation　of　waves　due　to　a　parabolic　shoal,　a　circular　island　mounted　on　a　paraboloidal　shoal　and　elliptic　shoal　situated　on　a　slope,　as　well　as　breakwater　gap.　The　results　were　compared　with　experimental　data,　analytical　solutions　and　other　numerical　methods,　and　reasonable　agreements　have　been　achieved.　©　2017　Elsevier　Ltd