Abstract: Current model for remaining useful life prognostic is usually based on the historical data, which can provide evidence for maintenance. However, singularity arising in the degradation data frequently give rise to a bad decline in prediction accuracy, this phenomenon is a great challenge for the time series prediction. To address this issue, we develop a new surrogate modeling prognostic approach based on cubic non-polynomial spline model in this paper. Meanwhile, due to the singularity perturbation in degradation tendency, the spline model's second derivative can be adopted and calculated to form a series of observation frames, and then a weighted hidden Markov model (HMM) method combined with particle swarm optimization (PSO) is used to forecast the observation sequence, then rebuild the spline function. A simulation example and a practical application involving typical singularities verified the effectiveness of the proposed method.