induces a large and tunable normal-mode splitting that enables microwave storage. When the spectral bandwidth of a short microwave pulse covers the two dressed-state absorption peaks, part of the pulse is absorbed and undergoes coherent energy exchange between the modes, producing a clear time-domain beating signal. By switching off the modulation before the beating arrives, we realize on-demand storage and retrieval, demonstrating an alternative approach to microwave photonic quantum memory. This parametric-normal-mode-splitting protocol offers a practical route toward a controllable quantum-memory mechanism in superconducting circuits.