In　this　paper,　we　present　an　experimentally　feasible　protocol　to　generate　the　cat　states　in　the　microwave　resonator　coupled　to　a　superconducting　qubit.　The　setup　employs　a　detuned,　time-dependent　parametric　drive　to　squeeze　the　resonator　mode　so　that　an　adjustable　qubit-resonator　coupling　strength　can　be　obtained.　Therefore,　based　on　the　transitionless　tracking　algorithm,　we　can　design　control　pulses　to　generate　the　qubit-resonator　entangled　states　with　high　fidelity　in　the　laboratory　frame.　Then,　the　even　and　odd　cat　states　can　be　further　obtained　by　performing　measurement　on　the　superconducting　qubit.　Compared　to　the　scheme　[Chen　et　al.,　Phys.　Rev.　Lett.　126,　023602　(2021)],　the　present　protocol　is　realized　in　the　regime　of　weak　parametric　drive.　In　the　case,　squeezing-induced　noise　can　be　reduced　so　that　the　fidelity　of　the　generated　state　can　be　improved.　Numerical　simulations　indicate　that　the　present　protocol　is　well　executed　under　experimentally　available　parameters.　Thus,　the　protocol　is　feasible　with　the　present　state　of　the　art　in　microwave　superconducting　circuits.