Concentration polarization and surface fouling may be two of the most remarkable features in the pressure-driven membrane filtration process. A new numerical simulation model is proposed in this paper to study the concentration polarization (CP) and the inorganic fouling growth. The numerical study is based on the lattice Boltzmann method (LBM), which allows a simultaneous solution of the Navier-Stokes equations and the convection-diffusion equation. Simulation results are verified by comparisons with published CP and permeate flux data under the same operating conditions. Then the model is extended to predict CP in a spacer filled desalination channel. The prediction result indicates that there is a higher fouling potential near the spacer filaments due to higher CP values in that area. Coupling of the CP prediction model with gypsum growth kinetics provides an approach to study the inorganic fouling growth on the membrane surface at a single crystal level, with respect to a given solution supersaturation near the membrane surface. Predicted equivalent radius and accumulated mass of the growing gypsum crystal, under the effects of growth retardation by bicarbonate, agree with published test data and analytical results. The presented numerical model enables a direct evaluation of the impacts on the surface crystal development in the presence of antiscalants. This numerical model can be applied to identify suitable operating conditions, assist in dose selection of antiscalants when required properties are available, and predict the fouling mitigation effects in the pressure-driven membrane filtration process.