Three to five μm mid-infrared laser has broad applications in atmospheric communication, environmental monitoring, medical treatment, and defense. Here, a series of glasses with compositions of 70TeO₂-25ZnO-5La₂O₃, doped with Dy³⁺ or Yb³⁺, and co-doped with Dy³⁺/Yb³⁺, were prepared using the melt-quenching method in an inert atmosphere-protected glovebox. Thermal properties, structural characteristics, hydroxyl content, and mid-infrared luminescence of the glasses were characterized through measurements such as differential scanning calorimetry (DSC), X-ray diffraction (XRD), Raman spectra, transmission spectra, and 3 μm band fluorescence spectra. The results indicate that 70TeO₂-25ZnO-5La₂O₃ glass possesses high resistance to crystallization (ΔT=101 ℃) and low phonon energy (760 cm^-1). Under 980 nm laser diode (LD) excitation, Dy³⁺/Yb³⁺ co-doped tellurite glass produces a broadband fluorescence emission around 3 μm region, with a full width at half maximum (FWHM) of 326 nm. This is attributed to the high energy transfer efficiency from Yb³⁺ to Dy³⁺ (98.74%) and the low hydroxyl absorption coefficient near 3 μm (0.32 cm^-1). Based on Judd-Ofelt and Dexter theories, spontaneous radiative transition probability, fluorescence branching ratio, and other spectroscopic parameters of Dy³⁺ ions, as well as microscopic parameters of Yb³⁺→Dy³⁺ energy transfer, were calculated. The primary energy transfer pathway is analyzed and identified as Yb³⁺: ²F_5/2→Dy³⁺: ⁶H_7/2, ⁶F_9/2. This study demonstrates that the low-hydroxyl Dy³⁺/Yb³⁺ co-doped TeO₂-ZnO-La₂O₃ glass can serve as an excellent 3 μm mid-infrared gain medium.