In non-volatile memory technology, various attempts to overcome both technology and physical limits have led to development of neuromorphic devices like memristors. Moreover, multilevel resistance and the potential for enhanced memory capability has attracted much attention. Here, we report memristive characteristics and multilevel resistance in a hydrogen annealed ZnO nanowire device. We find that the memristive behavior including negative differential resistance arises from trapped electrons in an amorphous ZnO interfacial layer at the injection electrode that is formed following hydrogen annealing. Furthermore, we demonstrate that it is possible to control electrons trapping and detrapping by the controlled application of voltage pulses to establish a multilevel memory. These results could pave the way for multifunctional memory device technology such as the artificial neuromorphic system.