In this paper, we firstly formulate a new hyperchaotic Hamiltonian system and demonstrate the existence of multi-equilibrium points in the system. The characteristics of equilibrium points, Lyapunov exponents and Poincaré sections are studied. Secondly, we investigate the complex dynamical behaviors of the system under holonomic constraint and nonholonomic constraint, respectively. The results show that the hyperchaotic system can generated by introducing constraint. Additionally, the hyperchaos control of the system is achieved by applying linear feedback control. The numerical simulations are carried out in order to analyze the complex phenomena of the systems.