A　protocol　for　complete　and　nondestructive　atomic　Bell-state　analysis　by　using　inverse　engineering　is　presented.　The　setups　for　the　Bell-state　analysis　contain　four　atoms　trapped　in　four　separated　cavities,　respectively.　The　laser　pulses　designed　by　inverse　engineering　help　in　the　manipulation　of　the　transitions　of　atoms　in　a　robust　manner.　By　using　the　protocol,　the　information　for　distinguishing　four　Bell　states　of　two　information-carrying　atoms　is　encoded　on　two　auxiliary　atoms.　Therefore,　the　four　Bell　states　can　be　distinguished　without　being　destroyed　by　detecting　the　states　of　the　two　auxiliary　atoms.　Moreover,　as　shown　by　the　numerical　simulations,　the　protocol　has　high　successful　probabilities　to　distinguish　four　Bell　states　when　decoherence　is　considered.　Thus,　the　protocol　may　provide　some　helpful　perspectives　for　the　quantum　information　tasks　based　on　Bell　states.