Associative learning, a critical learning principle to improve an individual's adaptability, has been emulated by few organic electrochemical devices. However, complicated bias schemes, high write voltages, as well as process irreversibility hinder the further development of associative learning circuits. Here, by adopting a poly(3,4-ethylenedioxythiophene):tosylate/Polytetrahydrofuran composite as the active channel, we present a non-volatile organic electrochemical transistor that shows a write bias less than 0.8 V and retention time longer than 200 min without decoupling the write and read operations. By incorporating a pressure sensor and a photoresistor, a neuromorphic circuit is demonstrated with the ability to associate two physical inputs (light and pressure) instead of normally demonstrated electrical inputs in other associative learning circuits. To unravel the non-volatility of this material, ultraviolet-visible-near-infrared spectroscopy, X-ray photoelectron spectroscopy and grazing-incidence wide-angle X-ray scattering are used to characterize the oxidation level variation, compositional change, and the structural modulation of the poly(3,4-ethylenedioxythiophene):tosylate/Polytetrahydrofuran films in various conductance states. The implementation of the associative learning circuit as well as the understanding of the non-volatile material represent critical advances for organic electrochemical devices in neuromorphic applications.