Improvement in efficiency and reliability are essential for more intensive deployment and exploitation of solid oxide fuel cell (SOFC) systems in modern society. Having the information about current health, degradation rate, and estimated remaining useful life (RUL) of the stack, at all times during operation, can greatly benefit the control system performance. Such information can be beneficial also for the service providers and end-users as the maintenance needs, including stack replacements, can be planned in advance. The control system can be able to optimize performance through a trade-off between maximal life span and best efficiency of power conversion. The knowledge on health status and its anticipated evolution assures easy and cost-effective maintainability. However, works that address issue of RUL prediction for SOFC are scant. On top of that, most of authors define voltage as health index and predict RUL accordingly. Such a selection of health index becomes inappropriate when SOFC is working under varying load conditions. In such a case stack voltage becomes affected by the changes in operating conditions and it is difficult to correlate drop in voltage with degradation rate. In this paper, we propose a novel hybrid approach to RUL prediction of SOFC systems, which overcomes the limitations of the known approaches and allows for reliable RUL prediction in non-stationary operating conditions. The approach consists of three main modules: (i.) estimation of area specific resistance (ASR) of the stack, (ii.) prediction of its future progress based on collected data, and (iii.) prediction of RUL. The methodology is evaluated on a 6 kW SOFC system.