Pressure dependence of electronic structures and thermoelectric properties of Mg2Sn are investigated by using a modified Becke and Johnson (mBJ) exchange potential, including spin-orbit coupling (SOC). The corresponding value of spin-orbit splitting at Γ point is 0.47 eV, which is in good agreement with the experimental value 0.48 eV. With the pressure increasing, the energy band gap first increases, and then decreases. In certain doping range, the power factor for n-type has the same trend with energy band gap, when the pressure increases. Calculated results show that the pressure can lead to significantly enhanced power factor in n-type doping below the critical pressure, and the corresponding lattice thermal conductivity near the critical pressure shows the relatively small value. These results make us believe that thermoelectric properties of Mg2Sn can be improved in n-type doping by pressure. Thermoelectric material by using the Seebeck effect can convert waste heat directly to electricity to solve energy problems. The performance of thermoelectric material can be characterized by dimensionless figure of merit [1,2], ZT = S 2 σT /(κ e + κ L ), where S, σ, T, κ e and κ L are the Seebeck coefficient, electrical conductivity, absolute temperature, the electronic and lattice thermal conductivities, respectively. Bismuthtellurium systems [3,4], silicon-germanium alloys [5,6], lead chalcogenides [7,8] and skutterudites [9,10] have been identified as excellent thermoelectric material for thermoelectric devices. For thermoelectric research, the main objective is to search for high ZT materials, which has proven to be interesting and challenging.The thermoelectric material Mg 2 X(X = Si, Ge, Sn) composed of abundant, low-cost elements and their alloys have attracted much recent attention [11][12][13], and various doping strategies have been adopted to attain high ZT [14][15][16]. Pressure by tuning the electronic structures of materials can accomplish many interesting phenomenons like recent pressure-induced high-Tc superconductivity in (H 2 S) 2 H 2 [17,18]. Here, we use first-principle calculations and Boltzmann transport theory to address the pressure dependence of thermoelectric properties in the Mg 2 Sn. Calculated results show that the pressure dependence of energy band gap with mBJ+SOC is consistent with one with mBJ [19], and first increases, and then decreases. Pressure can significantly improve power factor in n-type doping below the critical pressure. It is found that pressure can reduce the lattice thermal conductivity in certain pressure range. These lead to enhanced ZT , and make Mg 2 Sn become more efficient for thermoelectric application in n-type doping by pressure. So, pressure tuning offers a very effective method to search for materials with enhanced thermoelectric properties.The rest of the paper is organized as follows. Firstly, we shall give our computational details. Secondly, weEnergy ( The energy band gap (Gap) and the value of spin-orbit splitting at Γ point (∆so) as a function of pressure...