The degradation prediction of equipment is a crucial task in Prognostics and Health Management. This paper proposes an integrated method for data-driven prognosis based on Hidden Semi-Markov Models (HSMM) with kernel methods. However, unlike the assumption of a mixture of Gaussian distribution of emitting probability, we approximate the probabilities of multidimensional condition monitoring data as a linear combination of kernel functions. This method can achieve high-dimensional function fitting with limited parameters. Then, the procedures of parameter re-estimation and kernel center selection are developed. The reliability of equipment is estimated by the posterior probabilities. Finally, we give an integrated framework including offline training and online prediction processes. Some experiments are conducted on an open dataset of aircraft engines. Compared with other HSMM-based methods, it shows that the proposed method is more accurate and credible in RUL prediction. The shape of a mixture of kernels approximation is different from the Gaussian-type of distribution, which impacts the parameters of the degradation model. Therefore, the proposed method can identify a short-term warning state.