In this work, we developed flexible polymer-based memristive-like devices specifically designed for biosensing applications. The fabricated devices consist of two gold electrodes connected by a biocompatible polymeric resistive layer made of poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS) and poly(vinyl alcohol) (PVA), on flexible polyimide substrate. To demonstrate the applicability of this novel sensing approach for critical diagnostic applications, we explored the current-voltage (I-V) hysteretic properties for the detection of prostate-specific antigen (PSA). To ensure sensitivity, we harnessed the adhesive properties of 3-glycidyloxypropyl trimethoxysilane (GOPS), to coat the surface of PEDOT:PSS-PVA and then grafted anti-PSA antibodies covalently in the polymeric channel. The layer-by-layer assembly was monitored using electrochemical and current-voltage memristive-like measurements. The specific anti-PSA antibodies assembled on the memristive-like channel enabled PSA detection in undiluted high ionic strength solutions within concentration ranging from 0.005 to 50 ng/ml. Our thin-film organic memristive-like devices show promise as cost-effective building blocks for memristive-like biosensing of PSA at clinically relevant levels (ng/ml).