In neuromorphic computing networks, a flexible synaptic memristor with high recognition accuracy is highly desired. In this study, ZnO nanosheets (ZnO NS) embedded within a polymethyl methacrylate host material are used as the intermediate layer to prepare flexible synaptic memristor at a low-temperature of 80 °C. The device shows excellent switching characteristics with low SET/RESET voltages (−0.4 V/0.4 V) and stable retention characteristic (10 4 s). By modulating the conductance continuously, the flexible synaptic memristor simulates typical synaptic plasticities, including excitation post-synaptic current, paired-pulse facilitation, and spike-timing dependent plasticity. Especially, the neuromorphic system built from flexible ZnO NS-based memristors achieves a high recognition accuracy up to 97.7% for handwriting digit. Under the influence of 5% Uniform noise and 5% Gaussian noise, recognition accuracies are maintained at 94.6% and 93.7%, respectively. These properties are well maintained even when bending 1000 times at a radius of 5 mm. The flexible ZnO NS-based memristor shows great prospects in wearable devices and neural morphology calculation.