To investigate the mixed convection flows through nano-fluid in a square double lid-driven cavity with various inclination angles, a numerical method based on the finite volume approach is applied. In This paper Sio2/water nano-fluid have been used. The cavity is un-uniformly heated from the left, Th, and cooled from the opposite wall; the top and the bottom moving walls have been supposed to be insulated. The study has been executed for the Richardson number 0.1 to 10, Reynolds number 1 to 100 while solid volume fraction (φ) of nano-particles altered from 0 to 0.06. The impact of angle of inclination, solid volume fraction of nano-fluids, velocity of moving walls and Richardson number on hydrodynamic and thermal characteristics have been studied and discussed. As a result, it was found that the heat transfer increase with increase in solid volume fraction for a particular Reynolds. Also in higher Richardson, the effect of solid volume fraction increases on thermal behavior and flow pattern.