In　this　scheme,　based　on　the　weak　cross-Kerr　nonlinearity,　an　hyperconcentration　protocol　for　the　arbitrary　partially　hyperentangled　N-particle　Greenberger–Horne–Zeilinger　(GHZ)　state　is　presented.　Considering　the　N　photons　initially　in　the　nonmaximally　hyperentangled　GHZ　state　in　which　photons　are　entangled　simultaneously　in　the　polarization　and　the　spatial-mode　degrees　of　freedom,　we　can　obtain　the　maximally　hyperentangled　N-particle　GHZ　state　by　the　projection　measurements　on　the　additional　photons.　Numerical　simulation　demonstrates　that　by　iterating　the　entanglement　concentration　process,　we　can　improve　the　success　probability　of　the　scheme.　Furthermore,　we　discuss　the　feasibility　of　the　setups　of　the　protocol,　concluding　that　the　present　protocol　is　feasible　with　existing　experimental　technology.　All　these　advantages　make　this　scheme　more　efficient　and　more　convenient　in　quantum　communication.　©　2016,　Springer　Science+Business　Media　New　York.