Proton　exchange　membrane　fuel　cell　(PEMFC),　as　a　promising　power　source,　provides　a　feasible　solution　for　clean　and　low-carbon　energy　systems.　The　durability　problem　restricts　PEMFC　application　in　some　scenarios,　which　can　be　improved　by　the　prognostic　technology　indirectly.　This　paper　aims　to　develop　a　data-based　method　to　implement　the　short-term　and　long-term　prognostic　simultaneously,　and　the　developed　long-term　prognostic　can　be　performed　without　future　operation　information.　First,　the　short-term　prognostics　of　five　multi-step　ahead　forecasting　strategies　are　proposed　and　compared　based　on　a　long　short-term　memory　(LSTM)　network.　Results　show　that　the　multi-step　input　and　multi-step　output　(MIMO)　with　LSTM　strategy　has　a　better　performance　in　the　short-term　prognostics　under　the　test　conditions　of　the　stationary　and　dynamic　current.　Then,　the　hyper-parameters　of　the　prediction　model　are　determined　by　an　evolutionary　algorithm.　Furthermore,　in　the　long-term　prognostics　regime,　the　variable-step　long-term　method　is　proposed　and　rectified　by　the　short-term　prognostics.　Finally,　the　developed　remaining　useful　life　(RUL)　prediction　is　compared　with　a　model-based　extended　Kalman　filter.　The　average　root　mean　square　error　results　for　the　short-term　prognostics　of　two　conditions　are　0.00532　and　0.00538,　respectively.　The　RUL　estimations　of　two　PEMFCs　named　FC1　and　FC2　are　given　with　95%　and　90%　confidence　intervals,　respectively.　Consequently,　the　proposed　method　can　achieve　acceptable　accuracies　in　the　short-term　prognostic,　the　long-term　prognostic,　and　the　RUL　prediction.　©　2021　Elsevier　Ltd