Er3+-doped fiber lasers operating at 2.7 mu m have attracted increasing interest because of their various important applications; however, the intrinsic self-terminating effect of Er3+ and the reliability of glass hosts hindered the development of Er3+-doped fiber lasers. Herein, the glass-forming regions of a series TeO2-Ga2O3-R2O (or MO) (R = Li, Na, and Rb; M = Mg, Sr, Ba, Pb, and Zn) glasses are predicted by the thermodynamic calculation method. On this basis, the physical and optical properties of TeO2-Ga2O3-ZnO (TGZ) glass are investigated in detail as an example. Under the excitation of 980 nm laser diode, the fluorescence intensity at 2.7 mu m reaches a maximum in the heavily Er3+-doped TGZ glass. By contrast, the accompanying near-infrared fluorescence at 1.5 mu m and upconversion green emissions at 528 nm and 546 nm are all effectively weaken. Furthermore, the lifetime gap between the I-4(11/2) upper laser level and I-4(13/2) lower laser level is sharply narrowed from 2.81 ms to 0.59 ms, which is beneficial to overcome the population conversion bottleneck. All results demonstrate that these newly developed ternary tellurite glass systems are promising candidates for near-/mid-infrared laser glass fiber, fiber amplifiers, and fiber lasers.