The surface Pb-210 is one of the main background sources for dark-matter-search experiments using NaI(Tl) crystals, and its spectral features associated with the beta-decay events for energies less than 60 keV depends on the depth distribution of Pb-210 in the surface of an NaI(Tl) crystal. Therefore, we must understand the profile of surface Pb-210 to precisely model the background measurement in the low-energy region for the low-background experiment using NaI(Tl) crystals. We estimate the depth profile of the surface Pb-210 contamination by modeling the measured spectrum of the alpha emission from the decay of Po-210 at the decay sequence of the surface Pb-210 contamination that is obtained using an Rn-222-contaminated crystal. In order to describe the energy spectra of the surface contamination we perform a log-likelihood fit of the measured data to a sum of Geant4 Mote Carlo simulations, weighted by an exponential curve as a function of the surface depth. The lowand high-energy events from the beta decay of surface Pb-210 are also modeled to improve the depth profile for shallow depths. We simulate the energy spectra from beta decays of Pb-210 that are exponentially distributed in the surface by following two exponential functions where the mean-depth coefficients are free parameters in the data fitting; we observed that the energy spectra are in good agreement with the measured data. (C) 2020 Elsevier B.V. All rights reserved.