In view of the limitation of the traditional GM(1,1) model for prediction in practical engineering application, the coupling prediction model of the grey GM(1,1,t^α) and self-memory principle is constructed based on the grey GM(1,1,t^α) with time power. The traditional grey model’s weakness as being sensitive to initial value can been overcomed by the self-memory principle of the dynamic system. And the grey GM(1,1,t²) self-memory model is used to fit and forecast the settlement of soft soil foundation of a certain coastal highway, which can obtain satisfactory accuracy of fitting and forecasting. Experiment results show that the proposed model can improve the fitting and forecasting accuracy of the traditional grey prediction model remarkably.