Quantum　phase　transition　and　quench　dynamics　in　the　Jaynes-Cummings　model　with　squeezed　light　are　investigated.　We　find　a　special　unitary　transformation　that　removes　the　nonintegrable　squeezing　interaction　when　the　qubit　frequency　far　outweighs　the　field　frequency.　The　eigenenergies　and　the　eigenstates　of　the　normal　and　superradiant　phases　are　derived　analytically.　We　demonstrate　that　the　system　exhibits　a　second-order　quantum　phase　transition　at　a　phase-boundary-induced　nonlinearly　by　squeezed　light.　This　phase　boundary　requires　neither　an　ultrastrong　coupling　regime　nor　multiqubits,　which　lessens　the　difficulty　of　the　experiment.　The　entanglement　entropy　is　very　close　to　its　maximum　value　as　the　squeezing　strength　increases　in　the　superradiant　phase.　In　quench　dynamics,　the　nonlinear　relation　between　the　residual　energy　and　the　squeezing　strength　is　obtained　analytically.　©　2022　American　Physical　Society.