In this article the natural convection of nano-fluid water - copper in a square cavity has been studied numerically. The left wall is maintained at high temperature ,right wall is maintained at low temperature and the other walls are adiabatic. The numerical model is based on the SIMPLE algorithm is used to solve the equations of continuity, momentum and energy . The effects of pertinent parameters such as the position and length of the baffle, Rayleigh number and solid volume fraction, on the thermal performance of the cavity are examined. The results showed that, the increase of the Rayleigh number and volume fraction of nanoparticle increased the average Nusselt on both hot and cold walls. The results also showed that the average Nusselt numbers on cold wall increased and on hot wall decreased with increase of the baffle length.