We　present　a　numerically　stable　one-point　quadrature　rule　for　the　stiffness　matrix　and　mass　matrix　of　the　three-dimensional　numerical　manifold　method　(3D　NMM).　The　rule　simplifies　the　integration　over　irregularly　shaped　manifold　elements　and　overcomes　locking　issues,　and　it　does　not　cause　spurious　modes　in　modal　analysis.　The　essential　idea　is　to　transfer　the　integral　over　a　manifold　element　to　a　few　moments　to　the　element　center,　thereby　deriving　a　one-point　integration　rule　by　the　moments　and　making　modifications　to　avoid　locking　issues.　For　the　stiffness　matrix,　after　the　virtual　work　is　decomposed　into　moments,　higher-order　moments　are　modified　to　overcome　locking　issues　in　nearly　incompressible　and　bending-dominated　conditions.　For　the　mass　matrix,　the　consistent　and　lumped　types　are　derived　by　moments.　In　particular,　the　lumped　type　has　the　clear　advantage　of　simplicity.　The　proposed　method　is　naturally　suitable　for　3D　NMM　meshes　automatically　generated　from　a　regular　grid.　Numerical　tests　justify　the　accuracy　improvements　and　the　stability　of　the　proposed　procedure.