The surface complexation modeling of metal adsorption to birnessites is in its infancy compared to the charge-distribution multisite ion complexation (CD-MUSIC) models for iron/aluminum (hydr)oxides. Therefore, using X-ray diffraction with Rietveld refinement to obtain the reactive sites and their densities, a CD-MUSIC model combined with a Stern-Gouy-Chapman electrical double layer (EDL) model for the external surface and a Donnan model for the interlayer surface is developed for birnessites with different Mn average oxidation state (MnAOS). Proton affinity constants and the charge distributions of Pb surface complexes were calculated a priori. By fitting Pb adsorption data to the model the obtained equilibrium constants (log KPb) of Pb complexes were 6.9-10.9 for the double-corner-sharing and double-edge-sharing Pb2+ complexes on the edge sites and 2.2-6.5 for the triple-corner-sharing Pb2+ complex on the vacancies. The larger log KPb value was obtained for higher MnAOS. Speciation calculations showed that with increasing MnAOS from 3.67 to 3.92 the interlayer surface contribution to the total Pb2+ adsorption increased from 43.2% to 48.6%, and the vacancy contribution increased from 43.9% to 54.7%. The vacancy contribution from interlayer surface was predominant. The present CD-MUSIC-EDL model contributes to understand better the difference in metal adsorption mechanism between birnessite and iron/aluminum (hydr)oxides.