In recent years, yellow laser crystals have raised great attentions owing to their comprehensive applications in the fields such as laser display, laser medical treatment, light detection and ranging (LIDAR), Bose-Einstein condensates, and atomic cooling and trapping. With the development of commercial blue light LD, the direct pumping of Dy³⁺ doped laser crystals has realized yellow laser based on its transition ⁴F_9/2→⁶H_13/2. In this work, Dy³⁺: Y₃Al₅O₁₂ (Dy: YAG) crystals with 0.5%, 1.0%, 2.0%, 3.0%, and 4.0% (atomic fraction) nominal concentration of Dy³⁺ were grown using Czochralski method, the reason of crystal crack was discussed. Based on Judd-Ofelt (J-O) theory, the J-O intensity parameters and utilization, and other laser parameters of Dy: YAG crystals with different doping concentrations were evaluated. The effect of the doping concentration of Dy³⁺ on the spectroscopic performances like fluorescence branching ratio, stimulated emission cross-section, quantum efficiency, were analyzed comprehensively. Among all the five crystals, 1.0% Dy: YAG has the largest stimulated emission cross-section for 582 nm yellow emission, an intense fluorescence intensity with the 447 nm excitation, and a longer decay time of 0.823 ms. The fluorescence intensity and stimulated emission cross-section of 2.0% Dy: YAG are slightly less than that of 1.0% Dy: YAG, but the former has a higher absorption coefficient. Hence, the spectroscopic analysis results show that 1.0% and 2.0% are the suitable concentrations of Dy³⁺ ion in YAG crystal for yellow laser operation by diode pumping. The continuous wave laser with peak at 582.5 nm and the maximum output power of 166.8 μW yellow laser operation were realized in 2.0% Dy: YAG crystal.