The method to increase the core diameter of a crystal waveguide laser with high beam quality is theoretically investigated and experimentally verified. Through the simulation calculation of the relative gain of each guiding mode and considering the mode competition, the fundamental mode cut-off thickness of the core layer can reach 360 μm, twice of that by the traditional calculation method, when 1.0% Yb∶YAG is used as the core material and 0.5% Er∶YAG is used as the inner cladding material. A crystal waveguide with a core size of 400 μm×320 μm×77 mm is fabricated by diffusion bonding, and a waveguide laser is constructed. The maximum output power of this waveguide laser is 31 W, the conversion efficiency from light to light is 55.3%, and the near-diffraction-limited laser output with beam quality of 1.2×1.05 is obtained. The experimental results show that it is reliable to calculate the core diameter of the fundamental mode of a crystal waveguide by mode competition.