Artificial synapses with synaptic plasticity that mimic the bio-synaptic function are the main components of the neuromorphic computing system. In this study, we fabricated a memristor device, with organic functional material such as poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) using a solution-process method under air ambient with low temperatue <110 °C. By adjusting the volume ratios (2:1, 1:1, and 1:2) of different commercial-grade PEDOT:PSS (AI4083 and PH1000), three different devices with a structure of ITO/AI4083:PH1000/Al were fabricated. Among these devices, the ITO/AI4083:PH1000(1:1)/Al memristor device exhibited excellent and repeatable bipolar resistive switching characteristics with >500 endurance cycles and long retention time >10⁴ s with an ON/OFF ratio of >10. From I–V fitting, Ohmic conduction and Schottky emission were the main conduction mechanisms for low (ON) and high (OFF) resistance states, respectively. In addition, biological synaptic characteristics such as long-term potentiation, long-term depression, paired-pulse facilitation, and post-tetanic potentiation were successfully emulated. Finally, we performed pattern recognition simulations with measured data from the ITO/AI4083:PH1000(1:1)/Al device with the CIFAR-10 dataset using a three-layer neural network (8192 × 1024 × 10) and provided a recognition accuracy of 80%. These results indicate that our PEDOT:PSS-based device can be a promising application for bio-inspired neuromorphic systems.