A new hybrid composite containing cerium oxide nanoparticle (CeO2NP) and gold nanoparticle (AuNP)-decorated functionalized glassy carbon microspheres (FGCM) was synthesized (Au/CeO2@FGCM). As a result, an Au/CeO2@FGCM-paraffin oil paste electrode (PE) (Au/CeO2@FGCM-PE) was fabricated and employed for the voltammetric sensing of quercetin (QRT). The structure and surface morphology of Au/CeO2@FGCM were studied by X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Cyclic voltammetry (CV), square wave voltammetry (SWV) and electrochemical impedance spectroscopy (EIS) were employed for the investigation of the electrochemical behavior of Au/CeO2@FGCM-PE. Under the optimum conditions, the SWV oxidation peak current showed linear dependence on the QRT concentration in the range from 48 nM to 1.09 μM. The achieved limits of detection and quantitation were 0.37 nM and 1.22 nM, respectively. Au/CeO2@FGCM-PE was reproducible, sensitive and stable and displayed anti-interference ability for various common interferents. The proposed method was also successfully applied for real sample analysis. The QRT content extracted from natural sources was determined, and satisfactory results were achieved. Furthermore, the interaction of QRT with salmon testes and calf thymus dsDNA (st-DNA and ct-DNA) on Au/CeO2@FGCM-PE was studied by CV and SWV. The corresponding binding constant (K), surface concentration (Γ), and Gibbs free energy (ΔG°) were computed for the free QRT and the bound QRT-dsDNA complex. The calculated K values for the QRT-ct-DNA and QRT-st-DNA complexes were found to be 6.24 × 105 M-1 and 3.63 × 105 M-1, respectively, which revealed that QRT strongly interacted with ct-DNA compared to that with st-DNA. The decreased intensity of the QRT oxidation peak resulting from its interaction with dsDNA provides a chance to use QRT as a new indicator to analyze ct-DNA and st-DNA.