Building transient and flexible memristors is a promising strategy for developing emerging memory technologies. Here, a transient and flexible memristor based on a polymer nanocomposite, with a configuration of silver nanowire (AgNW)/citric acid quantum dot (CA QD)-polyvinyl pyrrolidone (PVP)/AgNW, is fabricated using a full-solution process method. The obtained device exhibits reversible resistive switching behavior and a dynamic random access memory (DRAM) storage feature, with the significant merits of a high ON/OFF ratio, low switching voltage, excellent reproducibility and desirable high flexibility, indicating outstanding memory characteristics such as low misreading, low power operation and low cost potential. Moreover, an operating mechanism of charge trapping/de-trapping of the quantum dots in the polymer matrix has been proposed. Importantly, the memristor can be disintegrated in water within 30 minutes, showing that it is a promising candidate for transient memories. This work paves a new way for potential use of this material in transient electronics, implanted electronics, data storage security and flexible electronic systems.