The　peridynamics　method　has　great　advantages　in　solving　crack　propagation　problems　due　to　its　automatic　tracking　of　crack　tips　by　breaking　bonds，but　it　also　faces　the　problems　such　as　numerical　oscillations　and　boundary　errors.　In　order　to　solve　the　above　defects，this　paper　first　discussed　the　NOSB-PD　method　with　the　meshless　Galerkin　weak-form　framework.　Next，it　introduced　the　peridynamics　differential　operator　approximation　and　fully　compared　and　analyzed　the　difference　between　the　PDDO　approximation　and　the　reproducing　kernel　particle　method（RKPM）approximation.　Then，it　proposed　the　RKPM-PD　coupling　algorithm　with　a　higher　numerical　accuracy　and　gave　the　implicit　iterative　process　of　the　RKPM-PD　method.　Finally，it　verified　the　effectiveness　of　the　algorithm　in　solving　three-dimensional　crack　propagation　problems　by　using　several　numerical　examples.　©　2022　Science　Press.　All　rights　reserved.