In this work, a reliable bilayer flexible memristor is demonstrated using TaOx/HfOx Bi-layer (BL) to mimic synaptic characteristics by using oxygen concentration engineering in the oxide layers. Due to low Gibbs free energy of TaOx layer and stable properties of the single layer memristor, TaOx is inserted in the HfOx-based memristor for making the BL flexible device. Such device exhibits stable gradual switching behavior with low set/reset voltages (1 V/−1 V) and multilevel cell characteristic making it favorable for synaptic application. The presence of oxide layers and change in oxygen vacancy concentration in two layers are examined by transmission electron microscopy and X-ray photoelectron spectroscopy, respectively. Further, the device shows potentiation and depression epochs for more than 10 000 pulses and switching up to bending radius of 4 mm for 1000 bending cycles. The device mimics biological synaptic time-dependent plasticity (STDP) operation when presynaptic and postsynaptic pulses are applied on top and bottom electrodes, respectively. The relationship between nonlinearity coefficient and control parameters in STDP is derived and established. It achieves more that 96% accuracy only after 20 iterations for neuromorphic application when a system of 2500 synapses incorporating 50 × 50 pixel image for recognition is deployed.