A novel nanoporous carbon material (NPC) was prepared by simple pyrolysis of an isoreticular metal–organic framework-8 (IRMOF-8) at 1000 °C. The obtained NPC possessed a three-dimensional hierarchy of micro-, meso-, and macropores, a high surface area of 1715 m2 g−1 and a large pore volume of 1.70 cm3 g−1. By using Nafion and bismuth films as co-modifiers, the obtained NPC was further used for the fabrication of a sensitive NPC–Nafion/bismuth composite modified glassy carbon electrode (NPC–Nafion/Bi/GCE) for electrochemical determination of Pb(II) in aqueous solution. The synergistic effect of the Nafion and Bi films, as well as the high activated surface area, hierarchical porous texture, and good electrical conductivity of the NPC contributed to the enhanced electrochemical response of Pb(II) at the NPC–Nafion/Bi/GCE during differential pulse anodic stripping voltammetry. Under the optimum conditions, the fabricated electrode exhibited two linear ranges varying from 1–7 μg L−1 and 7–70 μg L−1, respectively. The detection limit was estimated to be 0.8 μg L−1 (at a signal-to-noise ratio of 3) for Pb(II), which was about 12 times lower than the guideline value set by the World Health Organization (WHO) for drinking water. The NPC–Nafion/Bi/GCE showed high reproducibility, with relative standard deviations of 6.2% and 3.4% for multiple successive measurements of 10 and 50 μg L−1 Pb(II), respectively. The composite electrode was successfully used in the analyses of Pb(II) in tap-water samples, and good recoveries were obtained for various spiked values.