Lead (Pb) and cadmium (Cd) are toxic heavy metals commonly found in aqueous environments. Biochar as a green adsorbent generated from biomass feedstock may be used for effective removal of these heavy metals. This study investigated the adsorption kinetics and isotherms of Pb2+ and Cd2+ in aqueous solutions at different pH by biochar prepared from banana stem and leaf (BSL-BC) at 400 °C. Characterizations using scanning electron microscope, X-ray diffraction, and Fourier-transform infrared spectroscopy showed that the synthesized BSL-BC had rough surface, porous structure, and oxygen-containing functional groups. The adsorption of Pb2+ and Cd2+ onto BSL-BC reached equilibrium in 8 h and 200 min, respectively, with faster adsorption attained at higher pH and the optimum pH occurred at 5 (Pb2+) and 8 (Cd2+). All adsorption kinetic data followed the pseudo-second-order rate model. The adsorption isotherm data of Pb2+ and Cd2+ could be well-described by the Langmuir and Freundlich models, respectively, whereas neither the Temkin or Dubinin–Radushkevich models provided satisfactory fitting results. The maximum adsorption capacities for Pb2+ and Cd2+ were 302.20 and 32.03 mg/g, respectively. The calculated mechanism contributions showed that complexation with oxygen-containing functional groups, ion exchange, mineral precipitation, and Pb2+/Cd2+-π coordination accounted for 0.1%, 8.4%, 88.8%, and 2.6% to Pb2+ adsorption, and 0.4%, 6.3%, 83.0%, and 10.4% to Cd2+ adsorption, respectively. Therefore, mineral precipitation was likely the major mechanism responsible for adsorption of both Pb2+ and Cd2+ by BSL-BC. The results suggest that the synthesized BSL-BC has great potential for adsorption of Pb2+ and Cd2+ from aqueous solutions.