Ferroelectric tunnel junctions (FTJs) as the artificial synaptic devices have been considered promising for constructing brain-inspired neuromorphic computing systems. However, the memristive synapses based on the flexible FTJs have been rarely studied. Here, we report a flexible FTJ memristor grown on a mica substrate, which consists of an ultrathin ferroelectric barrier of BiFeO₃, a semiconducting layer of ZnO, and an electrode of SrRuO₃. The obtained flexible FTJ memristor exhibits stable voltage-tuned multi-states, and the resistive switchings are robust after 10³ bending cycles. The capability of the FTJ as a flexible synaptic device is demonstrated by the functionality of the spike-timing-dependent plasticity with bending, and the accurate conductance manipulation with small nonlinearity (−0.24) and low cycle-to-cycle variation (1.77%) is also realized. Especially, artificial neural network simulations based on experimental device behaviors reveal that the high recognition accuracies up to 92.8% and 86.2% are obtained for handwritten digits and images, respectively, which are close to the performances for ideal memristors. This work highlights the potential applications of FTJ as flexible electronics for data storage and processing.