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A forecasting procedure is proposed for plate boundary earthquakes in subduction zones. It is based on spatio-temporal variation in slip velocity on the plate interface, which causes interplate earthquakes. Model outputs are not only information about the occurrence of great earthquakes (time, place, and magnitude) but also information about the physical state evolution that causes earthquakes. To overcome the difficulty in forecasting earthquake generation resulting from uncertainty both in the physical model and in the observation data, we introduce a type of sequential data assimilation. In this method, we compare observed crustal deformation data to simulations of several great interplate earthquake generation cycles. We are currently constructing a prototype, applying this forecasting procedure to the Nankai Trough, Southwest Japan, where great interplate earthquakes have occurred and are anticipated.