On June 12, 1978, a large earthquake (M=7.4) occurred off the Pacific coast of Miyagi prefecture, northeastern Japan. The earthquake killed 28 persons and caused extensive damage in Miyagi prefecture. The previous large earthquake occurred in this region on November 3, 1936. Therefore, a next large earthquake is expected in this region in near future. It is important to estimate the slip distribution of both the 1978 and 1936 events in order to discuss a possible rupture area of the next event. In this paper, we estimate the slip distribution of the 1978 Miyagi-oki event using the tsunami waveforms observed at 12 tide gauge stations along the Pacific coast of northeastern Japan. Previously, the rupture process of the 1978 Miyagi-oki earthquake was estimated using the seismological data (eq. Seno (1980)). Seno (1980) show that the focal mechanism of the earthquake is a thrust type and the seismic moment is 3.1x10**20Nm. The event was separated into two subevents, one ruptured the eastern (trench-ward) part and the other ruptured the western (landward) part of the aftershock area. We numerically compute the tsunami waveforms using the finite-difference computation for the linear long-wave equations. The grid size is basically 20 sec of arc (about 600m), but finer grids (4 sec of arc) are nested near the tide gauge stations. Tsunami waveforms at 12 stations are computed for two subfaults (the western and eastern parts) with a unit amount of slip, and use as the Green's function for the inversion. The subfault size is 30km X 30km. The result of the inversion shows that the slip amounts of the western and eastern parts are about 1.3 m and 1.0 m, respectively. The total seismic moment is calculated as 1.4 X 10**20Nm (Mw=7.4) assuming that the rigidity is 5 X 10**10 N/m**2. This estimate is smaller than the seismic moment estimated from seismological data. The slip amount in the western subfault is larger than that in the eastern subfault. This slip pattern is consistent with the previous result. It will be interesting to estimate the slip pattern of the 1936 event and compare it with the slip pattern of the 1978 event in this study.