In this paper, we investigate the memristor properties of ZnO microstructures synthesized by hydrothermal method. ZnO is a promising material for obtaining energyefficient memory elements due to its compatibility with CMOS technologies, low cost, and good scalability. In this study, hexagonal ZnO microprisms with a diameter of ~10 μm and a thickness of ~2 μm were obtained. The study of the current-voltage characteristics revealed a unipolar memristor effect with switching between the high (HRS) and low (LRS) resistance states when applying both positive and negative voltage. The switching ratio ION/IOFF was 102 for forward bias and 104 for reverse bias. The obtained results demonstrate the potential of ZnO structures for application in non-volatile memory with low power consumption.