In this paper， a non standard Hamilton equation called the power-law Hamilton equation， is obtained by applying the isochronous variational method to the power-law Hamilton action. These equations are used to describe a special class of dynamical system. There is a controllable parameter γ in the power-law Hamiltonian equation. We can change the trajectories of motion of bodies or the behaviors of dynamical systems by adjusting γ. Some examples demonstrate that the power-law Hamiltonian systems have characteristics different from the standard ones， and some additional features are discussed in detail.