Artificial synapses, with synaptic plasticity, are the key components of constructing the neuromorphic computing system and mimicking the bio-synaptic function. Traditional synaptic devices are based on silicon and inorganic materials, while organic electronics can open up new opportunities for flexible devices. Here, a flexible artificial synaptic device with an organic functional layer was proposed. The organic device showed good switching behaviors such as ON/OFF ratio over 100 at low operation voltages. The set and reset voltages were lower than 0.5 V and −0.25 V, respectively. The long-term plasticity, spike-timing-dependent plasticity learning rules (STDP), and forgetting function were emulated using the device. The retention times of the excitatory and inhibitory post-synaptic currents were both longer than 60 s. The long-term plasticity was repeatable without noticeable degradation after the application of five voltage pulse cycles to the top electrode. These results indicate that our organic flexible device has the potential to be applied in bio-inspired neuromorphic systems.