Quantum　phase　transition　and　entanglement　in　the　Rabi　model　with　a　squeezed　light　are　investigated.　We　find　a　special　unitary-transformation　method　that　removes　the　nonintegrable　squeezing　and　counterrotating-wave　interactions　when　the　qubit　frequency　is　close　to　the　field　frequency.　The　analytical　ground　state　agrees　well　with　the　numerical　solution.　We　demonstrate　that　the　ground　state　exhibits　a　first-order　quantum　phase　transition　at　a　critical　point　induced　linearly　by　the　squeezed　light.　This　quantum　phase　transition　requires　neither　multiple　qubits　nor　an　infinite　ratio　of　qubit　frequency　to　field　frequency,　which　solves　a　critical　problem　for　the　theory　and　experiment　in　Rabi　model.　As　the　qubit-field　coupling　strength　increases,　the　ground-state　entanglement　reaches　its　maximum　value　at　the　critical　point.　©　2023　IOP　Publishing　Ltd.