The spectra properties of Yb3+∶SrMoO4 crystal were investigated by employing the absorption and emission spectra. The strongest absorption is observed at 976nm in the absorption spectra. The absorption cross-section is 1.7110-20cm2 at 976nm. The absorption band has a FWHM of 71nm. The Stark energy levels of Yb3+ in Yb3+∶SrMoO4 crystal were obtained in the absorption spectra and low temperature emission spectra. The emission peak is at 1021nm. The emission band has a FWHM of 44nm. The emission cross-section calculated by the reciprocity method is 1.2410-20cm2 at 1021nm. The fluorescence lifetime of Yb3+∶SrMoO4 crystal is 878s by fitting the fluorescence decay curve. The laser parameters of Yb3+∶SrMoO4 crystal were calculated by the spectral data, the pump saturation intensity parameter is 4.35kW/cm2, the minimum fraction of Yb3+ ions that must be excited to balance the ground state absorption and the gain exactly is 10.08%, the minimum pump intensity is 0.44kW/cm2. For large absorption and emmision FWHM, long fluorescene lifetime and low laser threshold, Yb3+∶SrMoO4 crystal could be considered as a LD pumped laser gain material and used in femto-laser and tunable laser area.