This paper examines the hyperchaotic dynamical behaviors of a new chaotic system, and the numerical simulation results of the adaptive control and synchronization problems of the hyperchaotic system with unknown parameters are presented. The chaotic behaviors of the hyperchaotic system is investigated by detailed numerical simulations results, such as phase portraits, Lyapunov exponents, bifurcation diagrams, and Poincaré sections, power spectrum and return map. Base on the lyapunov stability theory we derive the adaptive control law that the trajectory of the hyperchaotic system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. In addition, the adaptive control law is also applied to achieve the state synchronization of two identical hyperchaotic systems. Moreover, the simulation results eventually indicate the validity of the proposed techniques.