MXenes are emerging two-dimensional (2D) nanomaterials composed of transition metal carbides/nitrides/carbonitrides with several atomic layers. However, due to the analogous metallic conductivity, their development in the field of electronic devices is restricted. Recently, various etching methods of MXenes lead to the surface terminals containing different functional groups, which provides opportunities for further modification of MXene nanosheets and makes it possible to apply them in the field of electronic memristors. At present, there are few researches about memristors on the basis of MXene-polymer hybrid materials. Here, we synthesize Ti3C2Tx-MXenes and adjust their content in an insulating polyvinyl alcohol (PVA) polymer for triggering memristive performance, which affords outstanding bipolar resistive switching behavior. The memristor exhibits the characteristics of low operating voltage, long retention time, high flexibility, and acceptable mechanical stability. In order to examine the switching mechanism of the device, the charge transport model simulation is implemented, which indicates that charge trapping effect is responsible for the non-volatile memristor performance of Ti3C2Tx-PVA hybrid material. This work provides a simple strategy for preparing MXene-polymer hybrid materials and broadens the prospects of 2D MXenes in the field of non-volatile memory applications.