In the present study, a laminar natural convection flow of $H_2O$-Cu nanofluid in a two dimensional enclosure has been investigated using a thermal lattice Boltzmann approach with the Bhatnagar-Gross-Krook (BGK) model. The effect of suspended nanoparticles on the fluid flow and heat transfer process have been studied for different controlling parameters such as particle volume fraction ($Phi$), Rayleigh number (Ra). For this investigation the Rayleigh number changes from 104 to 106 and volume fraction varied from 0 to 10% with three different particle diameters (dp), say 10 nm, 20 nm and 40 nm. It is shown that increasing the Rayleigh number (Ra) and the volume fraction of nanofluid causes an increase of the effective heat transfer rate in terms of average Nusselt number (Nu) as well as the thermal conductivity of nanofluid. On the other hand, increasing the particle diameter causes the decrease of the heat transfer rate and thermal conductivity. The result of the analysis are compared with experimental and numerical data both for pure and nanofluids and it is seen a relatively good agreement.