We　propose　a　scheme　for　preparation　of　the　N-dimension　spin　Greenberger–Horne–Zeilinger　state　by　exploiting　quantum　dots　(QDs)　embedded　in　microcavities.　Numerically　analysed　results　show　that　with　the　spin-selective　photon　reflection　from　the　cavity,　we　can　complete　the　scheme　assisted　by　one　polarized　photon　with　high　fidelity　and　100%　successful　probability　in　principle.　Furthermore,　the　set-up　is　just　composed　of　simple　linear　optical　elements,　delay　lines　and　conventional　photon　detectors,　which　are　feasible　with　existing　experimental　technology.　Moreover,　QDs　have　numerous　admirable　features　in　weak-coupling　regime,　which　are　practicable　in　realistic　cavity　quantum　electrodynamics　system　shown　by　previous　numerical　simulations　and　experiments.　Therefore,　our　scheme　might　be　realized　in　near　future.　©　2016　Taylor　&　Francis.