In this paper, bismuth subcarbonate (BiO)2CO3-reduced graphene oxide nanocomposite incorporated in Nafion matrix ((BiO)2CO3-rGO-Nafion) was synthesized and further applied, for the first time, in the sensitive detection of Pb(II) and Cd(II) by square-wave anodic stripping voltammetry (SWASV). The as-synthesized nanocomposites were characterized by energy-dispersive spectroscopy (EDS), Raman spectroscopy, scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS). (BiO)2CO3 composite plays a key role in the improvement of the detection sensitivity, which can form multicomponent alloy with cadmium and lead. Additionally, the unique structure of rGO can enlarge the surface area and provide abundant active sites. Moreover, Nafion incorporation in the nanocomposite can effectively increase the adhesion and mechanical strength of the film, and further improve the preconcetration ability due to the cation-exchange capacity of its abundant sulfonate groups. As expected, the (BiO)2CO3-rGO/Nafion nanocomposite-modified glassy carbon electrode ((BiO)2CO3-rGO-Nafion/GCE) achieved low detection limits of 0.24 μg/L for Pb(II) and 0.16 μg/L for Cd(II), in the linear range of 1.0–60 μg/L, and showed some excellent performance, such as high stability, good selectivity, and sensitivity. Finally, synthetic water samples were prepared and further used to verify the practicability of the (BiO)2CO3-rGO-Nafion/GCE with satisfactory results.