We　propose　an　alternative　scheme　of　shortcuts　to　a　quantum　controlled　phase　gate　in　a　much　shorter　time　based　on　the　approach　of　Lewis-Riesenfeld　invariants　in　cavity　quantum　electrodynamics　systems.　This　scheme　can　be　used　to　perform　a　one-qubit　phase　gate,　a　two-qubit　controlled　phase　gate,　as　well　as　a　multiqubit　controlled　phase　gate.　The　strict　numerical　simulations　demonstrate　that　the　total　operation　time　for　implementing　controlled　phase　gates　is　much　shorter　than　previous　schemes　and　very　robust　against　decoherence.　©　2015　American　Physical　Society.