Developing optoelectronic synaptic devices with low power consumption, broadband response, and biological compatibility is crucial to simulate the functions of optic nerve. Here, an organic synapse transistor based on C8-BTBT/PMMA/PbS quantum dots (PbS QDs) is fabricated, which has good stability, low power consumption (as low as 0.49 fJ per event under 800 nm near-infrared optical pulse), and broadband response from ultraviolet to near-infrared wavelengths. Based on the trap and release of photogenerated carriers by PbS QDs, a series of synaptic behaviors are simulated by the device. Furthermore, we use artificial neural network as the model to realize the recognition of facial feature image in the broad spectral range; the recognition rate reached 96.25% (350 nm ultraviolet), 92.14% (580 nm visible), and 90.03% (800 nm near-infrared). This work is beneficial for advancing the development of future artificial intelligence vision sensing.