Time-prediction methods based on monitoring the displacement of a slope are effective for the prevention of sediment-related disasters. Several models have been proposed to predict the failure time of a slope based on the creep theory of soil, which describes the accelerating surface displacements that precede slope failure. Fukuzono proposed an inverse-velocity method to predict the failure time. Fukuzono’s method has been widely adopted in practice because of its simplicity. However, the actual displacement of the slope is complicated due to the change in the rainfall intensity and the inhomogeneity of the surface layer, and it is not easy to specify the period when the surface displacement accelerates. In this study, we predicted the failure time of a sandy model slope under artificial rainfall using three methods based on Fukuzono’s model using all data from the start of monitoring onwards. The results showed that using all monitoring data results decreased the prediction accuracy and that the accuracy of the prediction improves if the period in which the acceleration of the surface displacement continuously increased could be extracted. Therefore, we extracted the period in which acceleration of the surface displacement continuously increased using a moving average method and predicted the failure time again. This resulted in improved prediction accuracy and the dispersion of the predicted results decreased.