Laser cooling and trapping of Yb3+:YAG nano-crystals has been theoretically investigated. It has been shown that in the system of Yb3+:YAG nano-crystals pumped at 1030 nm in the long wavelength tail of the Yb3+ absorption spectrum both internal and translational laser cooling processes take place. The internal laser cooling process based on anti-Stokes fluorescence serves as a supplementary process to translational cooling of rare-earth (RE) doped nano-crystals. The internal laser cooling process can help to reach lower equilibrium translational temperatures of RE-doped nano-crystals.