Tb2Ti2O7 (TTO) single crystal with dimensions of 20 × 20 × 16 mm3 was grown by the Czochralski method. Rietveld structure refinement of X-ray diffraction (XRD) data confirms that the compound crystallizes in the cubic system with pyrochlore structure. Transmission spectra, Magnetic circular dichroism (MCD) spectra, Faraday and inverse Faraday characteristics of TTO crystal have been measured and analyzed in detail. The results demonstrate that TTO crystal has high transmittance at 700-1400 nm waveband and a larger Verdat constant than that of TGG reported. Magnetic circular dichroism (MCD) spectra showed that the 4f→4f transitions of Tb3+ have significant contributions to the magneto-optical activity (MOA). In the time-resolved pump-probe spectroscopy, the rotation signals of the probe beam based on the inverse Faraday effect in magneto-optical crystal were observed at zero time delay, the full width at half maximum of the rotation and ellipticity signals can be as fast as ~500 fs, which indicates that TTO crystal can be a promising material for ultrafast all-optical magnetic switching.