The 2011 Tohoku-Oki earthquake (M9.0) occurred on March 11, 2011. Many studies have investigated the co-seismic slip distribution of the earthquake on the plate interface based on terrestrial seismological and geodetic data and seafloor geodetic data. However, since seafloor stations installed before the main shock were concentrated in the off Miyagi Prefecture area, the spatial extent of the area of very large slip on the shallow plate interface was not well constrained along the direction parallel to the Japan Trench. After the main shock, large post-seismic deformations were detected by the terrestrial Global Navigation Satellite System (GNSS) observation stations and the seafloor station network, which includes 20 new seafloor stations installed after the 2011 Tohoku-Oki earthquake. The post-seismic displacement rate field in the offshore area revealed that the viscoelastic relaxation in the asthenospheric layer beneath the earth’s elastic crust is the main cause of the post-seismic deformation not the afterslip on the plate interface. Since stress perturbation due to the co-seismic slip excited the viscoelastic relaxation, the post-seismic displacement rates provide information about the co-seismic slip. Therefore, it is possible to constrain the co-seismic slip distribution on the shallow plate interface near the Japan Trench, based on the post-seismic displacements by applying Green’s function, which includes viscoelastic displacement evolution. We simultaneously inverted co- and post-seismic displacement data to estimate the co- and post-seismic slip distributions of the 2011 Tohoku-Oki earthquake with better spatial resolution than models based on the elastic Green’s function. The result indicates that the shallow co-seismic rupture extended maximally from 37.0°N to 39.2°N near the Japan Trench. Afterslip distribution was also well constrained in comparison to previous studies because of the introduction of the newly established GNSS-Acoustic observation network.