Although many studies have been continuously conducted to reduce the power consumption of a resistive random access memory (RRAM) cross-point array with the current-compliance effect, it has been difficult yet to realize intrinsic self-compliance effects in an RRAM device itself. In this study, a simple oxygen-rich TiOy layer is inserted into the Al2O3/TiOx-based RRAM stack as a current suppression layer, and XPS analysis is provided to compare the stoichiometry of the TiOx and TiOy layers. A self-compliance region is formed between the different breakdown voltages of Al2O3 and TiOy layers, and a relatively thinner current path is formed in the Al2O3 layer than a device without the TiOy layer and the overall current level is significantly decreased since the TiOy layer limits the overshoot current.