This paper presents a similarity-based approach for the prediction of the Remaining Useful Life (RUL) of sea water filters placed upstream the heat exchangers of a nuclear reactor condenser. The prognostic approach is developed considering a library of reference degradation trajectories containing parameter observations taken from a set of similar equipments until their failures. The prediction of the RUL of the a filter is obtained by comparing its degradation trajectory to the reference trajectories and by properly aggregating the RULs of the training trajectories using a weighted sum which takes into account the similarity within test and training trajectories. In order to provide a measure of confidence in the RUL prediction in the form of a prediction interval, we place our work within the framework of belief function theory and we assign to each reference trajectory a belief proportional to its similarity to the test trajectory. A prediction interval is then obtained by properly combining these belief assignments using the Dempster's rule.