We show that graphene quantum dots (GQD) embedded in a semiconducting poly(3-hexylthiophene) polymeric matrix act as charge trapping nanomaterials. In plane current-voltage (I-V) measurements of thin films realized from this nanocomposite deposited on gold interdigitated electrodes revealed that the GQD enhanced dramatically the hole transport. I-V characteristics exhibited a strong nonlinear behavior and a pinched hysteresis loop, a signature of a memristive response. The transport properties of this nanocomposite were explained in terms of a trap controlled space charge limited current mechanism.