Based　on　fractional　calculus　predictor-corrector　algorithm,　the　fractional-order　hyperchaotic　Chen　system　is　investigated　numerically,　and　the　simulation　results　show　that　the　lowest　orders　for　hyperchaos　in　hyperchaotic　Chen　system　gets　3.8.　According　to　the　stability　theory　of　fractional-order　system,　an　improved　state-observer　is　designed,　and　the　response　system　of　generalized　synchronization　is　obtained　analytically,　whose　feasibility　is　proved　theoretically.　The　synchronization　method　is　adopted　to　realize　the　generalized　synchronization　of　3.8-order　hyperchaotic　Chen　system,　and　the　numerical　simulation　results　verify　the　effectiveness.