Abstract: The authors investigate Casimir functions on Pseudo-Poisson manifold and one necessary and sufficient condition is obtained for the existence of Casimir functions on Pseudo-Poisson manifold.As an application,by using Casimir functions,how to construct a corresponding augment generalized Hamiltonian system and the maintenance of energy-conservation are also concerned.

Key words: Pseudo-Poisson manifold, Casimir function, generalized Hamiltonian system of control, energy-conservation