An organometallic compound, [(CH₃)₄N]₂[Cu(dmit)₂] (dmit^2-=4,5-dithiolate-1,3-dithiole-2-thione), abbreviated as MeCu is synthesized. Its nonlinear optical absorption properties dissolved in acetone with concentration of 2×10^-3 mol/L are studied using the open-aperture Z-scan technique with 40 ps pulse width at 1064 nm and 15 ns pulse width at 1053 nm, respectively. The sample shows two-photon absorption when irradiated by 40 ps pulse at 1064 nm and the two-photon absorption coefficient is 4×10^-13 m/W. While excited by 15 ns laser pulses at 1053 nm, strong reverse saturable absorption is found and the nonlinear absorption coefficient is estimated to be as high as 7.07×10^-11 m/W. The nonlinear absorption properties of the sample at different laser intensities and the optical limiting with 15 ns pulse at 1053 nm are also measured. All the results suggest that this material may be a promising candidate for the optical limiting application.