Buoyancy driven heat transfer of Cu-water nanofluid in a differentially heated square cavity with an inner adiabatic square baffle at different positions is studied numerically. The left and right walls of the cavity are at temperatures of Th and Tc, respectively that Th > Tc, while the horizontal walls are insulated. The governing equations are discretized using the finite volume method while the SIMPLER algorithm is used to couple velocity and pressure fields. A parametric study is conducted and effects of Rayleigh number (103 to 106), the position of the baffle (six different positions), and the volume fraction of nanoparticles (0 to 0.1) on flow pattern, temperature distribution and heat transfer inside the cavity are investigated. The obtained results show that the rate of heat transfer is enhanced with increase of both Rayleigh number and volume fraction of nanoparticles. Moreover it is found that based on the Rayleigh number, the effect of position of the baffle on the rate of heat transfer varies. At all Rayleigh number considered, when the baffle is located in the core of the cavity, maximum rate of heat transfer occurs. Also the position of the baffle has a minimum effect on the rate of heat transfer at Ra = 106.