We have experimentally studied the multilevel resistive switching in forming-free nanocrystalline ZnO films. It was shown that potentiation and depression at 0.5 V and ‒0.5 V for 3000 cycles led to the film resistance increasing by 3 orders of magnitude. In addition, it was shown that ZnO films successfully mimic biological memory through increased pulse number stimulation. Fixing the amplitude of the training pulses makes it possible to achieve different resistive states such as synaptic weight levels of the biological brain. The obtained results can be used for ReRAM elements of neuromorphic artificial intelligence systems fabrication based on forming-free nanocrystalline ZnO films.