This paper presents an interval prediction algorithm based on grey system modelling, which is proposed for the forecasting of strong-oscillation time series with small samples. In the proposed algorithm, the upper and lower envelope of an oscillating sequence is obtained through cubic spline interpolation, and distance between the envelope and the fitted sequence derived from grey system model is dynamically expanded according to the oscillation intensity. After that, prediction value of the envelope distance sequence is calculated, and adjusted adaptively based on the new information priority principle. Finally, the interval prediction result is obtained. To verify the performance of the algorithm, five application cases from different fields were adopted. Compared with five representative algorithms in the recently related field, the proposed algorithm has distinct advantages in the prediction of small-sample strong-oscillation time series. © 2019 Inderscience Enterprises Ltd.