Organic material-based memristive devices are regarded as the most promising for bio-implantable devices due to their bio-compatibility and flexibility. Particularly, polymers in the form of solid polymer electrolytes have gained a lot of attraction due to their low-cost and easy synthesis process. This work presents studies of memristive devices based on copper-ion conductive polymer electrolytes (Cu-SPEs) as a switching medium, where copper and ITO are used as the top and bottom electrodes, respectively. The thickness of the Cu-SPE films is found around 950 nm. We fabricated memristive devices by varying the weight percentage of copper (II) triflate salt with respect to polyethylene oxide (PEO). The current–voltage (I-V) behavior of the fabricated memristive devices depends on the copper (II) triflate concentration in the switching medium. All these devices show non-volatile bipolar switching behavior. The memristive device with 1 wt. % of copper (II) triflate shows lowest SET and RESET voltages (VSET = 280 mV and VRESET = − 170 mV). The ON/OFF resistance ratio is approximately 104. The switching mechanism is the electrochemical metallization (ECM) process, where formation and rupture of the copper nano-filament are governed by electrochemical redox reaction at the interface. These memristive devices hold promises for developing low-power memory devices (bio-memristors) due to very low programming voltages (SET and RESET voltages).