Based on the density functional theory and the Boltzmann transport theory, the thermoelectric properties of $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution with $x = 0.25, 0.5$ and $075$ were investigated. The calculated structural parameters were in good agreement with the previous work and the mechanical and dynamical stabilities were confirmed. The electronic band structure computed using the Tran-Blaha-modified Becke and Johnson (TB-mBJ) exchange potential indicated that the band gap can be tuned by the alloy effect. We combined first-principles calculations and the semiclassical Boltzmann transport theory by considering the electronic transport in the $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution to determine the effect of varying the Sn composition on the thermoelectric performance. Our results have shown exceptionally high electrical conductivity for $\rm{Mg_{2}Sn}$ and higher Seebeck coefficient for $\rm{Mg_{2}Si}$. The highest figure of merit (ZT) was predicted for $\rm{Mg_{2}Si_{1−x}Sn_{x}}$ solid solution with x = 0.5 where ZT has reached 0.55 with carrier concentration charge $n = 10^{20} \rm{cm}^{−3}$ (p-type doping) at intermediate temperatures. Consequently, the alloying system with p-type doping may improve the thermoelectric properties compared to the $\rm{Mg_{2}Si}$ and $\rm{Mg_{2}Sn}$ pristine compounds.