The　design　of　a　fuzzy　neural　network　(FNN)　has　long　been　a　challenging　problem　since　most　methods　rely　on　approximation　error　to　train　an　FNN,　which　may　easily　result　in　overfitting　phenomenon　to　degrade　the　generalization　performance.　To　improve　the　generalization　performance,　an　FNN　with　a　multiobjective　optimization　algorithm　(MOO-FNN)　is　proposed　in　this　article.　First,　the　multilevel　learning　objectives　are　designed　around　the　generalization　performance　to　guide　the　training　process　of　an　FNN.　Then,　the　method　utilizes　the　approximation　error,　the　structure　complexity,　and　the　output　smoothness　indicators　instead　of　a　single　indicator　to　improve　the　evaluation　accuracy　of　generalization　performance.　Second,　an　MOO　algorithm　with　continuous-discrete　variables　is　developed　to　optimize　the　FNN.　Then,　MOO　is　able　to　use　a　novel　particle　update　method　to　adjust　both　the　structure　and　parameters　rather　than　adjusting　them　separately,　thereby　achieving　suitable　generalization　performance　of　the　FNN.　Third,　the　convergence　of　MOO-FNN　is　analyzed　in　detail　to　guarantee　its　successful　applications.　Finally,　the　experimental　studies　of　MOO-FNN　have　been　performed　on　model　identification　of　nonlinear　systems　to　verify　the　effectiveness.　The　results　illustrate　that　MOO-FNN　has　a　significant　improvement　over　some　state-of-the-art　algorithms.