Nowadays there is a growing interest in wearable and biocompatible computing systems that are safe for the human body. Memristive devices are prospective for such tasks owing to a number of their attractive properties, in particular, the multilevel character of resistive switching, or plasticity, which allows them to emulate synapses in hardware neuromorphic networks (NNs). The use of local learning rules for such NNs, for example, bioinspired spike-timing-dependent plasticity (STDP), has firmly established itself in recent years. In biological systems the basic STDP can be modified in the presence of neuromodulators (e.g. dopamine). This effect is believed to be essential for important biological functions such as reinforcement learning (RL), memory and others. The goal of this work was to demonstrate that such dopamine-like modulated STDP can be used in memristors based on a biocompatible polymer, parylene (poly-p-xylylene, or PPX). We have studied memristors both in the form of single Cu/PPX/ITO devices and in the form of crossbar Cu/PPX/Au structures. It was found that, in addition to stable memristive characteristics suitable for NNs, these devices can also change their conductance by means of bioinspired STDP rules, including dopamine-like modulated STDP window realized by introducing the coefficients for neuron spike amplitudes. The amplitude coefficients from −1 (inhibitory mode) to 1 (excitatory mode) of pre-and post-spikes, reflecting the 'dopamine' concentration, in various combinations allow observing the STDP window not only of the usual shape, but also of the anti-STDP, bell and anti-bell shapes. The obtained results demonstrate that the development of memristors based on PPX provides prospects for hardware realization of bio-inspired spiking NNs with RL ability.