Using discrete method, N,N-Dimethylformamide (DMF) and tetrahydrofuran(THF) are adopted as solvent to fabricate MoS2 suspension solution, and its nonlinear optical properties in the visible and near infrared region are studied by open aperture Z-scan method. The results show that under the intense laser, in MoS2 (in DMF) suspension solution, saturable absorption property can be detected in the visible waveband (530 nm), showing that its transmittance is 1.54 times of ordinary, and reverse saturable absorption can be observed in the near infrared region (790 nm), indicating that its transmittance is 0.6 time of ordinary one and very good wavelength selection optical limiting effect. As a comparison, in the MoS2 (in DMF) suspension solution there does not appear the wavelength selection feature, but the reverse saturable absorption is present in all band. This phenomena may be produced through the two mechanisms: saturableabsorption and thermally-induced self-diffraction.