In　this　paper,　a　dynamic　system,　the　fractional-order　hyper-chaotic　complex　Lu　system　is　proposed　for　the　first　time　and　its　rich　dynamics　are　investigated　through　numerical　simulations.　It　is　found　that　the　variation　of　both　the　system　parameters　and　the　fractional　order　can　induce　bifurcations,　and　the　parameter　ranges　of　chaos　are　different.　Furthermore,　based　on　the　Open-Plus-Closed-Loop　(OPCL)　technique　and　the　stability　theory　of　fractional　order　dynamical　system,　a　scheme　of　modified　projective　synchronization　(MPS)　for　the　fractional　order　hyper-chaotic　complex　Lu　system　is　presented,　which　can　effectively　achieve　modified　projective　synchronization　in　a　class　of　high　dimensional　fractional　order　systems.　Examples　of　numerical　simulations　are　presented　to　show　the　validity　of　the　proposed　control　strategy.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.