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Er3+-doped and Yb3+/Er3+ co-doped Gd3Sc2Ga3O12 (abbreviated as Er:GSGG and Yb,Er:GSGG, respectively) laser crystals are investigated by using a combination of spectroscopic measurements and thermal characterizations. An absorption peak of Yb, Er: GSGG crystal shifts to 970 nm and its absorption band broadens obviously, which makes the crystal suitable for pumping by a 970 nm laser diode (LD). This crystal also exhibits a shorter lifetime of a lower laser level, a larger emission cross section and higher thermal conductivity than those of Er: GSGG. All these factors suggest that Yb3+/Er3+ co-doping has a positive effect on improving the spectroscopic and thermal performances in GSGG based laser crystals, and imply that double-doped Yb, Er: GSGG crystal is a potential candidate as an excellent LD pumped 2.79 mu m laser material.