A　weak　form　of　the　peridynamic　(PD)　method　derived　from　the　classical　Galerkin　framework　by　substituting　the　traditional　derivatives　into　the　PD　differential　operators　is　proposed.　The　attractive　features　of　the　proposed　weak　form　of　PD　method　include　the　following:　(1)　a　higher-order　approximation　than　the　non-ordinary　state-based　peridynamic　(NOSB-PD)　in　the　strain　construction;　(2)　the　NOSB-PD　is　demonstrated　as　a　special　case　of　the　weak　form　of　the　PD　method;　(3)　as　an　extension　of　the　NOSB-PD,　the　zero-energy　mode　oscillations　in　the　weak　form　of　the　PD　can　be　significantly　reduced　by　introducing　higher-order　PD　derivatives.　In　addition,　a　series　of　numerical　tests　are　conducted.　The　results　show　the　following:　(1)　the　three　proposed　stabilization　items　containing　higher-order　PD　derivatives　have　a　better　accuracy　and　stability　than　the　traditional　items　of　the　NOSB-PD.　In　particular,　the　stress　point　stabilization　item　is　preferred　since　it　has　the　highest　accuracy　and　efficiency　and　does　not　introduce　any　additional　parameters;　(2)　the　weak　form　of　PD　method　is　very　suitable　in　dealing　with　the　crack　propagation　and　bifurcation　problems.