Abstract: Some useful viewpoints on earthquake forecasting, based on Prof. Li Siguang 's important speeches and instructions, are presented in this paper in combination with authors'own experience and understanding. Those can be summarized in the four aspects as follows. The existence and change of earth stress has close relation with earthquake. Relatively safe areas may occur in active earthquake zones. Earthquake survey must be the basis of earthquake forecasting. Earthquake is predictable and the change process of earth stress is the key for earthquake forecasting. Professor Li Siguang's theory of "Safe Island" and the thought on earthquake forecast is of great significance both theoretically and realistically, which are the precious assets he left to us and worthy of further consideration, research and implementation so far.