Yb³⁺ doped (atomic number fraction of 5%) gadolinium-sodium-potassium molybdate laser crystal K_0.1Na_0.9Gd(MoO₄)₂ was grown by Czochralski method in this work. Then the crystal structure was characterized and the density, specific heat, thermal diffusivity and thermal conductivity were measured. Additionally, a simple and effective theoretical fitting method for specific heat and thermal diffusivity was proposed, and the fitting results were in good agreement with the experimental results. The results have shown that, the crystal belongs to tetragonal crystal system, with the structural characteristics of scheelite, the experimental density and theoretical density are 5.3792 g/cm³ and 5.3460 g/cm³, respectively, the Vickers hardness of the crystal along the $b$-axis is 251.5 kg/mm², and as the temperature increases, the thermal conductivity of the crystal decreases from 1.03 W⋅m^-1⋅K^-1 at 300 K to 0.91 W⋅m^-1⋅K^-1 at 400 K. The specific heat of the crystal at 300 K is about 0.62 J·g^-1·K^-1, indicating that the crystal has a high thermal damage threshold. Under the excitation of InGaAs laser diode with the wavelength of 970 nm, the strongest emission peak of the crystal appears at 1023 nm with bandwidth of 43 nm, indicating that the crystal is promising for broadband tunable and ultrashort pulse laser. The study of the mechanical, thermodynamic, and spectral properties of the crystal can provide an important reference for the study of its laser performance.