Absorption and fluorescence spectra of Er:GSGG crystal were measured and investigated. The oscillator strength, spontaneous emission probability, energy level lifetime, emission branching ratio and absorption cross-section of Er3+ transitions were calculated according to the Judd-Ofelt theory. It is found that the crystal has long lifetime at 4I13/2 and 4I11/2, large absorption cross-section at 965 nm and 790 nm, large stimulated emission cross-section at 2.79 μm. Laser output characteristics were simulated numerically with 965 nm pumping, where it has a large quantum efficiency when the pump rate reaches certain value. The results show that the crystal may be a suitable laser material at 2.79 μm wave band.