In this work we investigate the conductance quantization (QC or CQ) phenomenon in the Cu/Ta2O5/Pt resistive random access memory (RRAM) devices. The Ta2O5 film was deposited on Pt-Si substrate using RF magnetron sputtering, followed by patterning of Cu top electrodes. The devices demonstrate robust bipolar resistive switching behavior, with low set and reset voltages (< 1V), and high resistance contrast (~103 ), owing to the electrochemical metallization mechanism. Quantized conduction was observed during the reset operation with well-defined conduction steps. Conductance (G) histograms revealed Gaussian distribution of G/G0 around the integral and half-integral values, where G0 is the fundamental unit of conductance (77.6 μS). The maximum conductance state observed was 310G0. Moreover, the currentvoltage curves of QC reset cycles clearly revealed that multiple conduction states appear at the same current value which opens potential avenues for developing multi-state memory devices based on QC states. The findings in this work contribute to the understanding of quantized conduction in RRAM devices for non-conventional computing applications such as in-memory and neuromorphic computation.