The bulk tin selenide (SnSe) is the best thermoelectric material currently with the highest figure-of-merit due to strong phonon-phonon interactions. We investigate the effect of electron-phonon coupling (EPC) on the transport properties of a two-dimensional (2D) SnSe sheet. We demonstrate that EPC plays a key role in the scattering rate when the constant relaxation time approximation is deficient. The EPC strength is especially large in contrast to that of pristine graphene. The scattering rate depends sensitively on the system temperatures and the carrier densities when the Fermi energy approaches the band edge. We also investigate the magnetothermoelectric effect of the 2D SnSe. It is found that at low temperatures there is enormous magnetoelectrical resistivity and magnetothermal resistivity above 200%, suggesting possible potential applications in device design. Our results agree qualitatively well with the experimental data.