A flexible, non-enzymatic glucose sensor was developed and tested on a polyethylene terephthalate (PET) substrate. The sensor’s design involved printing Ag (silver) as the electrode and utilizing mixtures of either gold–copper oxide-modified reduced graphene oxide (Au-CuO-rGO) or gold–copper oxide-modified reduced graphene oxide-multi-walled carbon nanotubes (Au-CuO-rGO-MWCNTs) as the carrier materials. A one-pot synthesis method was employed to create a nanocomposite material, consisting of Au-CuO-rGO mixtures, which was then printed onto pre-prepared flexible electrodes. The impact of different weight ratios of MWCNTs (0~75 wt%) as a substitute for rGO was also investigated on the sensing characteristics of Au-CuO-rGO-MWCNTs glucose sensors. The fabricated electrodes underwent various material analyses, and their sensing properties for glucose in a glucose solution were measured using linear sweep voltammetry (LSV). The LSV measurement results showed that increasing the proportion of MWCNTs improved the sensor’s sensitivity for detecting low concentrations of glucose. However, it also led to a significant decrease in the upper detection limit for high-glucose concentrations. Remarkably, the research findings revealed that the electrode containing 60 wt% MWCNTs demonstrated excellent sensitivity and stability in detecting low concentrations of glucose. At the lowest concentration of 0.1 μM glucose, the nanocomposites with 75 wt% MWCNTs showed the highest oxidation peak current, approximately 5.9 μA. On the other hand, the electrode without addition of MWCNTs displayed the highest detection limit (approximately 1 mM) and an oxidation peak current of about 8.1 μA at 1 mM of glucose concentration.