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Gd₃ and Ga₃ co-doped garnet-type Yb_3-xGd_xAl_5-xGa_xO₁₂ solid solution (x=0.0,0.1,0.2,0.3,0.4,0.5;YGAGO) ceramic materials were synthesized by citric acid sol-gel method. XRD results demonstrate that all the Yb_3-xGd_xAl_5-xGa_xO₁₂ compositions are comprised of the pure garnet Yb₃Al₅O₁₂ phase. Increasing the Gd₃ and Ga₃ doping fractions leads to a shift of the X-ray spectrum to lower 2θ values. SEM morphology shows that microstructure is composed of nano-sized crystal grains and high densed grain boundary. The substitution of larger Gd₃ and Ga₃ in smaller Yb₃ and Al₆ sites, respectively, not only can lower the thermal conductivity, but also jontly facilitate higher coefficients of thermal expansion (CET), which is due to the relaxation of distored Yb_3-xGd_xAl_5-xGa_xO₁₂ structure with substitutional point defects. The phonon mean free path of Yb_3-xGd_xAl_5-xGa_xO₁₂ ceramics decreases with increasing Gd₃ and Ga₃ fraction at identical temperature levels, which is due to the lattice distortion and local imperfection scaling generated by incorporating large dopant Gd₃ and Ga₃ cations. Gd₃ and Ga₃ co-doped garnet-type Yb_3-xGd_xAl_5-xGa_xO₁₂ composition showed a minimum thermal conductivity value (λ=1.67W/m.K,T=1273K) and a maximum CET (ɑ_l=11.71×10_-6 K_-1,T=1273K) at the composition Yb_2.5Gd_0.5Al_4.5Ga_0.5O₁₂.