Optical communication is a particularly compelling technology to tackle the speed and capacity bottlenecks in data communication in modern society. Currently, silicon photodetector plays a dominant role in the high-speed optical communication across the visible-near infrared spectrum. However, its intrinsic rigid structure, high working bias, and low responsivity largely limit its applications in the next-generation flexible optoelectronic devices. Herein, we report a solution-processed flexible organic photodetector (OPD) based on a narrow-bandgap nonfullerene acceptors, which exhibits a remarkable response time of 91 ns and peaking responsivity of 0.53 A W-1 (λ = 830 nm) at zero bias, exceeding the values obtained in the state-of-the-art high-speed commercial Si photodetector (326 ns; 0.26 A W-1). This exceptional performance benefits from the low parasitic capacitance and high charge mobility due to low trap states and energetic disorder in the organic photoactive film. More significantly, the flexible OPD exhibits negligible performance attenuation (<1%) after bending for 500 cycles, and maintain 96% of its initial performance even after 550 h of indoor exposure. Furthermore, it also demonstrates a high data transmission rate of 80 MHz with a with a bit-error-rate of 3.5×10-4, offering great potential in next-generation high-speed flexible optical communication system.