By balancing energy transfer and thermal effects, we demonstrate efficient erbium-doped yttrium gallium garnet (Er:YGG) crystal lasers at a wavelength of 2.82-2.92 μm for the first time, to the best of our knowledge. Associated with the influence of doping concentration on energy transfer and thermal effects, the Er3+ doping concentration was optimized to be 10 at.%, and with the optimized crystal, the maximum continuous-wave output power was 1.38 W, corresponding to the slope efficiency of 35.4% approaching the theoretical quantum limits. The thermal effects during the laser process were discussed. We believe that this work should be helpful for optimizing the erbium-doped gain for the 3 μm laser and the development of 3 μm lasers.