In this paper, a passivity-based synchronization method is proposed for a new hyperchaotic Lorenz System based on Lyapunov stability theory and linear matrix inequality (LMI) approach. On the basis of the property of the passive system, the passive controller is designed and synchronization of two identical new hyperchaotic Lorenz systems with different initial conditions is realized. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed chaos control and synchronization schemes.