We　theoretically　present　a　protocol　to　realize　the　controlled　phase　gate　with　Cooper-pair　box　(CPB)　qubits　in　circuit　quantum　electrodynamics　(circuit　QED)　system.　In　this　protocol,　the　one-dimensional　transmission　line　resonator　in　circuit　QED　system　acting　as　quantum　data　bus　generates　a　common　cavity　mode　and　interacts　with　each　CPB　qubit.　The　Rabi　frequencies　of　driven　pluses　can　be　designed　with　simple　Gaussian　or　trigonometric　functions　by　utilizing　the　universal　SU(2)　transformation.　Moreover,　the　level　configurations　of　CPB　qubits　have　been　reported　by　previous　protocol(Feng　and　Zhang　in　Phys　C　470:240-243,　2010).　Thus,　the　protocol　can　be　realized　easily　in　experiment.　In　addition,　the　influence　of　various　decoherence　processes　such　as　spontaneous　emissions,　dephasings　of　the　CPB　qubits　and　the　decay　of　the　cavity　mode　on　the　fidelity　is　discussed　by　numerical　simulations.　The　results　show　that　the　protocol　is　robust　against　the　decoherence　and　parameter　variations.　Therefore,　the　protocol　may　be　useful　for　the　fields　of　quantum　computations.