We report on the non-volatile resistive switching properties of epitaxial nickel oxide (NiO) nanostructures, 10-100 nm wide and up to 30 nm high grown on (001)-Nb:SrTiO3 substrates. Conducting-atomic force microscopy on individual nano-islands confirms prominent bipolar switching with a maximum ON/OFF ratio of ∼103 at a read voltage of ∼0.4V. This ratio is found to decrease with increasing height of the nanostructure. Linear fittings of I-V loops reveal that low and high resistance states follow Ohmic-conduction and Schottky-emission mechanism, respectively. The switching behavior (dependence on height) is attributed to the modulation of the carrier density at the nanostructure-substrate interface due to the applied electric field.