We present a simple thermal treatment with antimony source for the MOCVD growth of thin GaSb films on GaAs (111) substrates for the first time. The properties of the as-grown GaSb films are systematically analyzed by scanning electron microscopy, atomic force microscopy, X-ray diffraction, photo-luminescence (PL) and Hall measurement. It is found that the as-grown GaSb films by the proposed method can be as thin as 35 nm and have a very smooth surface with the root mean square roughness as small as 0.777 nm. Meanwhile, the grown GaSb films also have high crystalline quality, of which the FWHM of the rocking-curve is as small as 218 arcsec. Moreover, the good optical quality of the GaSb films has been demonstrated by the low-temperature PL. This work provides a simple and feasible buffer-free strategy for the growth of high quality GaSb films directly on GaAs substrates and the strategy may also be applicable to the growth on other substrates and hetero-growth of other materials.