Ship height positioning by the Global Navigation Satellite System (GNSS) was investigated for measuring and forecasting great tsunamis. We first examined GNSS height-positioning data of a navigating vessel. If we use the kinematic precise point positioning (PPP) method, tsunamis greater than 10 −1 m will be detected by ship height positioning. Based on Automatic Identification System (AIS) data, we found that tens of cargo ships and tankers are usually identified to navigate over the Nankai Trough, southwest Japan. We assumed that a future Nankai Trough great earthquake tsunami will be observed by the kinematic PPP height positioning of an AIS-derived ship distribution, and examined the tsunami forecast capability of the offshore tsunami measurements based on the PPP-based ship height. A method to estimate the initial tsunami height distribution using offshore tsunami observations was used for forecasting. Tsunami forecast tests were carried out using simulated tsunami data by the PPP-based ship height of 92 cargo ships/ tankers, and by currently operating deep-sea pressure and Global Positioning System (GPS) buoy observations at 71 stations over the Nankai Trough. The forecast capability using the PPP-based height of the 92 ships was shown to be comparable to or better than that using the operating offshore observatories at the 71 stations. We suppose that, immediately after the occurrence of a great earthquake, stations receiving successive ship information (AIS data) along certain areas of the coast would fail to acquire ship data due to strong ground shaking, especially near the epicenter. Such a situation would significantly deteriorate the tsunami-forecast capability using ship data. On the other hand, operational real-time analysis of seismic/geodetic data would be carried out for estimating a tsunamigenic fault model. Incorporating the seismic/geodetic fault model estimation into the tsunami forecast above possibly compensates for the deteriorated forecast capability.