In this paper we present a numerical simulation of porous journal bearing behavior considering the fluid film - poroelastic matrix interaction and the non-Newtonian rheological behavior of a nano-lubricant consisting of a base fluid and nanoparticles (NPs). The flow of a nano-lubricant in the bearing clearance space is described by the micro-continuum theory of VK Stokes which considers the characteristic size of nanoparticles dispersed in a base oil. The flow of the nano-lubricant in the porous medium is modeled by a modified Darcy's law where the Beavers-Joseph slip condition is applied at the fluid film-porous matrix interface. The deformation of the porous matrix interface due to hydrodynamic pressure is calculated using the Winkler elastic thin layer model. The hydrodynamic behavior of the lubricating film is governed by a modified Reynolds equation obtained from the motion and continuity equations using the classical Reynolds derivation process. The bearing porosity is introduced into the Reynolds equation by means of the Morgan-Cameron approximation. The steady-state analysis shows that for an imposed eccentricity ratio, the load capacity increases with the characteristic size and the concentration of nanoparticles while the attitude angle, the leakage flow rate, and the coefficient of friction decrease. On the other hand, the permeability decreases the hydrodynamic pressure, the load capacity, and the leakage flow rate; but increases the attitude angle and the coefficient of friction.