Crystal waveguides prepared by adhesive-free bonding techniques demonstrate strong mode-limiting effects. In this paper, the crystal waveguide's single transverse mode condition is calculated in the context of mode competition. The single transverse mode thickness range of the core and inner cladding is obtained when the core material is Yb∶YAG with atomic number fraction of 1% and the inner cladding material is Er:YAG with atomic number fraction of 0.5%. Results from these calculations show that the maximum core thickness can be increased to approximately 1.79 times of the traditional calculation results obtained without mode competition. This finding provides theoretical support for the possibility of simultaneous large-mode area and single transverse mode output. A large-core Yb∶YAG crystal waveguide with a core size of 320 μm×400 μm is prepared in the experiment. The crystal waveguide is used as a gain medium to build a crystal waveguide laser that could output a 1030-nm laser. The laser's maximum output power is 26 W, with a slope efficiency of 31.5% and beam quality factors of Mx2=1.22 and My2=1.05. These experimental results demonstrate that the crystal waveguide can achieve an output that approaches the diffraction limit. The introduction of mode competition is a reliable design method for achieving single transverse mode output in a large-core crystal waveguide.