To investigate the convection in a porous medium, a horizontal quiescent layer of one fluid saturating a porous medium heated from bottom is numerically studied using single lattice-Boltzmann method (LBM) and the generalized Navier-Stokes equation proposed by Nithiarasu et al. [P. Nithiarasu, K.M. Seetharamu, and T Sundararajan, Int. J. Heat Mass Trans. 40 (1997) 3955]. Due to the rarefaction, the boundary conditions are considered as both temperature jump and velocity slip. The computational results are validated against the analytical results, and excellent agreement has been obtained. The results have shown that the Rayleigh number is increased with increasing temperature jump, the stabilization effect of temperature is much more significant than that of velocity slip, and the computation stability of present model is better than that of Darcy and Brinkman models.