The kinetics for NO reduction over supported platinum under lean condition were investigated by first-principles-based kinetic Monte Carlo simulation over three-dimensional Pt nanoparticles. Model platinum nanoparticles with diameters ranging from 2.3 to 4.6 nm were constructed using a truncated octahedral cluster consisting of a two (100) facets and eight (111) facets. First-principles density functional theory (DFT) calculations were used to calculate the intrinsic kinetic parameters including the binding energies for all of the surface intermediates as well as the activation barriers and reaction energies that comprise the reaction mechanism over the (100) and (111) facets, as well as the (111)/(100) edge sites on the three-dimensional nanoparticle. Both intra- and inter-facet diffusion of adsorbates were included to model surface diffusion effects over the particle surface. The simulation results show that under lean conditions where there is excess oxygen, NO reduction to N2 occurs solely on the (100) facets. The oxidation of NO to NO2, while much more favored on the (111) facets, can occur on both (100) and (111) facets. Only small amounts of N2O form over the (100) facets. The simulated apparent activation energies for N2 and NO2 formation over the entire particle are 45 and 42 kJ/mol, respectively. The latter is in agreement with experimentally measured value of 39 kJ/mol [Mulla, S. S., et al., Catal. Lett. 2005, 100, 267]. The effects of particle size on the activities of NO reduction to N2 and NO oxidation to NO2 depend upon the ratios of exposed surface sites. For the three-dimensional model Pt nanoparticles examined here, the fractions of the (100) terrace sites are similar while the fraction of the (111) terrace sites increases with increasing particle size. As a result, the activity for NO reduction is somewhat insensitive to the particle size which symmetrically increases the numbers of (111) and (100) facets as the size increases. NO reduction, however, increases much more dramatically when the number of the (100) sites increases over the (111) sites. NO oxidation activity, on the other hand, appears to increase with increasing particle size regardless of the symmetry or shape of the particle as the reaction occurs predominantly over the (111) sites but can also take place on the (100) terrace sites. The structure insensitivity for NO oxidation is consistent with experimental results.