The conduction mechanism of metal oxide resistive switching memory is debated in the literature. We measured the I-V characteristics below the switching voltages through TiN/HfOx/Pt memory stack and found the conduction cannot be described by the commonly used Poole-Frenkel model, because the fitted dielectric constant and the trap energy are unreasonable as compared to their known values. Therefore, we provide an alternate viewpoint based on a trap-assisted-tunneling model. Agreement of the bias polarity/temperature/resistance state-dependent conduction behavior was achieved between this model and experimental data. And insights for the multilevel capability due to the control of tunneling distance were obtained.