A 3D lattice Boltzmann model is developed and used to calculate the water and gas permeabilities of model cement pastes at different degrees of water saturation. In addition to permeable micron-sized capillary pores and impermeable solid inclusions, the lattice Boltzmann model comprises weakly-permeable nano-porous calcium silicate hydrate (C-S-H). The multi-scale problem is addressed by using an effective media approach based on the idea of partial bounce-back. The model cement paste microstructures are generated with the platform mu ic. The critical parameters, C-S-H density and capillary porosity, are taken from H-1 nuclear magnetic resonance relaxation analysis. The distribution of water and air is defined according to the Kelvin-Laplace law. It is found that when the capillary porosity is completely saturated with a fluid (either water or gas), the calculated intrinsic permeability is in good agreement with measurements of gas permeability on dried samples (10(-17)-10(-16) m(2)). However, as the water saturation is reduced, the calculated apparent water permeability decreases and spans the full range of experimentally measured values (10(-16)-10(-22) m(2)). It is concluded that the degree of capillary water saturation is the major cause for variation in experimental permeability measurements. It is further concluded that the role of the weakly-permeable C-S-H, omitted in earlier modelling studies, is critical for determining the permeability at low capillary saturation.