The lattice Boltzmann method (LBM) was used to study the three-dimensional (3D) mass diffusion of three species ($H2$, $H2O$, and $N2$) in the pore phase of a porous solid oxide fuel cell (SOFC) anode. The method used is an extension of a two-dimensional (2D) LBM model (2007, “**Lattice Boltzmann Method for Continuum, Multi-Component Mass Diffusion in Complex 2D Geometries**
,” J. Phys. D, 40, pp. 2961–2971) to study mass transport in SOFC anodes (2007, “**Lattice Boltzmann Modeling of 2D Gas Transport in a Solid Oxide Fuel Cell Anode**
,” J. Power Sources, 164, pp. 631–638). The 3D porous anode geometry is initially modeled using a set of randomly packed and overlapping solid spheres. Results using this simple geometry model are then compared with results for an actual SOFC anode geometry obtained using X-ray computed tomography (XCT) at sub-50 nm resolution. The effective diffusivity $Deff$ of the porous anode is a parameter, which is widely used in system-level models. However, empirical relationships often used to calculate this value may not be accurate for the porous geometry that is actually used. Solution of the 3D Laplace equation provides a more reliable and accurate means to estimate the effective diffusivity for a given anode geometry. The effective diffusivity is calculated for different geometries and for a range of porosity values, both for the 3D sphere packing model and for the real geometry obtained by XCT. The LBM model is then used to predict species mole fractions within the spherical packing model geometry and the XCT geometry. The mole fraction variation is subsequently used to calculate the concentration polarization. These predictions compare well with previously obtained 2D results and with results reported in the literature. The 3D mass transport model developed in this work can be eventually coupled with other transport models and be used to optimize the anode microstructure geometry.