The　dynamics　of　network　traffic　are　complex　and　nonlinear,　and　chaotic　behaviors　and　their　prediction,　which　play　an　important　role　in　local　area　networks　(LANs),　are　studied　in　detail,　using　the　largest　Lyapunov　exponent.　With　the　introduction　of　phase　space　reconstruction　based　on　the　time　sequence,　the　high-dimensional　traffic　is　projected　onto　the　low　dimension　reconstructed　phase　space,　and　a　reduced　dynamic　system　is　obtained　from　the　dynamic　system　viewpoint.　Then,　a　numerical　method　for　computing　the　largest　Lyapunov　exponent　of　the　low-dimensional　dynamic　system　is　presented.　Further,　the　longest　predictable　time,　which　is　related　to　chaotic　behaviors　in　the　system,　is　studied　using　the　largest　Lyapunov　exponent,　and　the　Wolf　method　is　used　to　predict　the　evolution　of　the　traffic　in　a　local　area　network　by　both　Dot　and　Interval　predictions,　and　a　reliable　result　is　obtained　by　the　presented　method.　As　the　conclusion,　the　results　show　that　the　largest　Lyapunov　exponent　can　be　used　to　describe　the　sensitivity　of　the　trajectory　in　the　reconstructed　phase　space　to　the　initial　values.　Moreover,　Dot　Prediction　can　effectively　predict　the　flow　burst.　The　numerical　simulation　also　shows　that　the　presented　method　is　feasible　and　efficient　for　predicting　the　complex　dynamic　behaviors　in　LAN　traffic,　especially　for　congestion　and　attack　in　networks,　which　are　the　main　two　complex　phenomena　behaving　as　chaos　in　networks.