Large third-order optical nonlinearity is observed in single-walled carbon nanotube (SWNT) films that are directly synthesized by CVD method rather than post-deposited from solution. Through z-scan method, the third-order nonlinear susceptibility (chi(3)) is measured, and the |Im chi(3)| is 1.8 x 10(-7) esu at 1064 nm, which is among the highest reported values for optical nonlinear materials. Combined with their transparent morphology and ultrafast carrier relaxation time, our results indicate the promising prospect of directly synthesized SWNT films as saturable absorbers using in mode-lock lasers or ultrafast switching materials in optical telecommunications.