The　generalized　hypercube　is　an　excellent　interconnection　network　since　it　includes　many　interconnection　topologies　and　it　can　be　used　to　construct　many　data　center　networks.　Considering　the　probability　that,　in　general,　all　neighbors　of　one　vertex　becoming　faulty　at　the　same　time　is　extremely　low,　we　assume　that　each　vertex　has　at　least　one　fault-free　neighbor.　An　r-dimensional　generalized　hypercube　is　denoted　by　G(m-r,　m-r-1,⋅,　m-1).　In　this　paper,　we　proposed　an　efficient　algorithm　which　can　construct　at　least　κ^1(G)　disjoint　paths　based　on　any　two　adjacent　vertices　in　G(m-r,　m-r-1,　m-1)　in　O(rm)　time　where　κ^1(G)　is　the　1-restricted　connectivity　of　G(m-r,　m-r-1,　m-1).　The　maximum　length　of　these　disjoint　paths　is　bounded　by　7.　©　2019　IEEE.