In this thesis, we have reviewed the Horava-Lifshitz gravity and the explained about motivation of the Horava to introduce this gravitational model and disscussed use of the Lifshitz scalar theory . In the following, the special symmetry of theory which is called "Foliation-Preserving Diffeomorphisms" has been expressed . For writting the action of this model, we have reviewed on the ADM formalism and introduced the quantites for this model. In the second chapter, the method of obtaining generators of the Diffeomorphism-indused gauge symmetries, which proposed by Pons and his colleagues in 1996, has been introduced . In this method, with use of the concept of projectibility, the generator of projectable transformations has been obtained. In third chapter, we have tried to find the generator of the Foliation-Preserving Diffeomorphisms via writing the Horava-Lifshitz gravitational Hamiltonian model . Finally, time reparametrization of this theory has been investigated via review of the Henneaux ’s paper .