Pollution from harmful heavy metal ions such as Pb(II) and Cu(II) is causing serious environmental and health problems. In this study, Sodium and nitrogen co-doped porous carbon material (Na/NABc) was successfully prepared from seaweed, sodium hydroxide, and dicyandiamide. The experimental results showed that Na/NABc is an excellent adsorbent for the effective removal of Pb(II) and Cu(II) from water bodies. Specifically, 99.8% of Pb(II) and 64.6% Cu(II) (100 mg/L) were removed within 12 h using 10 mg Na/NABc(10%) at 25 °C. The adsorption of Pb(II) and Cu(II) in aqueous solution by Na/NABc(10%) was efficient and rapid in the first stage. The theoretical maximum removal capacities of Na/NABc for Pb(II) and Cu(II) were 959.6 and 299.1 mg/g, respectively. Pb(II) and Cu(II) ions were adsorbed quickly in the first 60 min, and the kinetics data were generally consistent with a pseudo-second-order model. Na/NABc(10%) had a large distribution coefficient for Pb(II) (8.38 L/mg) and Cu(II) (1.17 L/mg). The possible mechanisms were precipitation, Ion exchange, and surface complexation. The removal rate can reach about 70% after five cycles, and the release of sodium meets the standard. The results of this study demonstrate the potential applicability of Na/NABc(10%) for adsorption of heavy metals from aqueous solution.