Based　on　the　Lu　chaotic　system,　a　new　four-dimensional　hyperchaotic　Lu　system　with　higher　order　nonlinear　term　is　constructed,　and　the　basic　dynamic　behaviors　of　the　system　are　studied.　The　Routh-Hurwitz　theorem　is　applied　to　derive　the　stability　conditions　of　the　proposed　system.　Further-more,　based　on　Lyapunov　stability　theory,　an　adaptive　controller　is　designed　and　the　new　four-dimensional　hyperchaotic　Lu　system　is　controlled　to　equilibrium　point.　Numerical　simulation　results　are　presented　to　illustrate　the　effectiveness　of　this　method.