In this paper, passive stability and synchronization analysis of a nonlinear fractional-dimension hyperchaotic system are discussed. By using the passivity theory, the effective controllers are designed for the globally asymptotic stability at the equilibrium point of the nonlinear fractional-dimension hyperchaotic system. The synchronization error dynamical system between two hyperchaotic systems is asymptotically stable under different initial values respectively. Furthermore, the corresponding numerical simulations verify the effectiveness of the proposed control and synchronization methods.