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We investigate theoretically a type of microwave memory that is composed of a single transmon qubit and a coupling resonator. The synergy of the parametric modulation of the qubit resonance frequency and a microwave directly driving the qubit transition can constitute effective three-level Λ-type electromagnetically induced transparency. We demonstrate that the dynamical control of such a parametric modulation allows for the possibility of microwave storage and retrieval using a single qubit. Our results pave the way towards the practical implementation of quantum information in superconducting circuits.