The electronic structures of monolayer and bilayer SnSe2 under pressure were investigated by using first-principles calculations with van der Waals interactions included. For monolayer SnSe2, the variation of electronic structure under pressure is controlled by pressure-dependent lattice parameters. For bilayer SnSe2, the changes in electronic structure under pressure are dominated by intralayer and interlayer atomic interactions. The n-type thermoelectric properties of monolayer and bilayer SnSe2 under pressure were calculated on the basis of the semi-classical Boltzmann transport theory. It was found that the electrical conductivity of mono- and bilayer SnSe2 can be enhanced under pressure, and such dependence can be attributed to the pressure-induced changes of the Se-Sn antibonding states in conduction bands. Finally, the doping dependence of power factors of n-type monolayer and bilayer SnSe2 at three different pressures were estimated, and the results unveiled that thermoelectric performance of n-type mono- and bilayer SnSe2 can be improved by applying external pressure. This study benefits to understand the origins of the transport properties for monolayer and bilayer SnSe2 under pressure, and it offers valuable insight for designing high-performance thermoelectric few-layer SnSe2 through strain engineering induced by external pressure.