Transient heat and mass diffusion and convection from porous structure walls are simulated by mesoscopic scale parallel non-dimensional lattice Boltzmann method (P-NDLBM) simulations. Mesoscopic dimensionless governing parameters have been obtained by scaling analysis. Dimensionless relaxation times for density, temperature, and concentration distribution factions are related to mesoscopic governing parameters. Various kinds of porous wall structures composed by one phase of solid and one fluid phase of air are generated by the Controllable Structure Generation Scheme (CSGS) based on discrete Gaussian quadrature space and velocity. The heat and mass transfer patterns affected by the different thermal and mass diffusivity of the solid phases and the fluid phase are also studied. The double diffusion effects of the random structure walls with various porosities are compared. The present results are expected to give some guidance on heat and mass transfer inside and away from various random constructed building walls.