Double diffusive natural convection in an enclosure filled with random porous media has been simulated by a Non-dimensional Lattice Boltzmann method (NDLBM). The random structures with different porosities are generated by a Controllable Structure Generation Scheme (CSGS). The NDLBM and the CSGS with mesoscopic scale governing parameters enable the direct simulations of transient velocity, temperature and concentration fields in pore scale for random media of a wide range of porosities. Validations of the parallel codes have been done by comparing to natural convection in a pure fluid filled enclosure obtained by various methods. Distributions of pore scale velocities, temperatures, and concentrations are quantitatively shown. Effects of the governing parameters on the macroscopic Nusselt, Sherwood and Biot numbers are presented. The changes of physical properties including solid fluid interface effects are also discussed.