The　reason　that　wavelet　basis　is　used　as　a　substitute　for　traditional　polynomial　basis　in　Element-Free　Galerkin　Method　(EFG)　is　analyzed　and　the　fundamental　is　expounded.　Comparisons　are　made　between　EFG　with　wavelet　basis　and　Finite　Element　Method　(FEM)　on　theories,　shape　functions,　displacement　boundary　conditions,　accuracy　and　applicable　areas.　Finally　the　feasibility　of　B-splines　wavelet　basis　in　EFG　and　the　advantage　of　this　method　are　verified　through　an　example.