With the view towards future non-volatile random access memories that can be integrated at a large scale, extensive study on resistive switching (RS) devices arranged in a crossbar array is currently underway. Although the crossbar array architecture offers relatively simple and acceptable scalability, the presence of sneak current is recognized as a critical issue that needs to be resolved at device level. In addressing this issue, we demonstrate a new type of RS device fabricated by combining graphene oxide (G-O) and zinc oxide (ZnO) with highly asymmetric current-voltage (I-V) characteristics depending on the polarity of bias voltage. The distinctive highly asymmetric I-V characteristics result from the presence of a hetero-junction interface formed between the G-O and ZnO layers. This hetero-junction manifests resistance in the range of GΩ under both forward and reverse bias voltage when the device is in the OFF state, in contrast, when the device is in the ON state, it exhibits resistance in the range of MΩ or kΩ under forward bias and GΩ under reverse bias. We propose to employ demonstrated RS devices with highly asymmetric I-V characteristics to mitigate adverse effects of the sneak current.