We demonstrate a flexible organic synaptic transistor (FOST) with an ion-composite electrolyte film resistant to chemical reagents, which uses a three-dimensionally cross-linked polyimide matrix to accommodate a high-concentration ionic liquid. FOST shows versatile synaptic plasticity for classical conditioning, high-pass filtering, and the learning-forgetting process. The device achieves low-energy consumption down to 1.02 femtojoule per synaptic event with an ultrasensitive impulse to presynaptic spike down to 0.5 mV. Moreover, the electrical performance of the device is still stable after 1000 mechanical bending cycles. These results demonstrate that the device can be applied to future flexible neuromorphic electronics.