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The memristive device is one of the basic elements of novel, brain-inspired, fast, and energy-efficient information processing systems in which there is no separation between memorization and information analysis functions. Since the first demonstration of the resistive switching effect, several types of memristive devices have been developed. In most of them, the memristive effect originates from direct modification of the conducting area, e.g. conducting filament formation/disintegration, or semiconductor doping/dedoping. Here, we report a solution-processed lateral memristive device based on a new conductivity modulation mechanism. The device architecture resembles that of an organic field-effect transistor in which the top gate electrode is replaced with an additional insulator layer containing mobile ions. Alteration of the ion distribution under the influence of applied potential changes the electric field, modifying the conductivity of the semiconductor channel. The devices exhibit highly stable current-voltage hysteresis loops and Short-Term Plasticity (STP). We also demonstrate short-term synaptic plasticity with tunable time constants.