This paper addresses the bidding strategies of a pumped-storage hydro plant in an electricity market. Competitive bidding of pumping and generating of a pumped-storage plant is formulated in a game theoretic problem in accordance with the three different ownership of scheduling; Market Operator(MO), generating company(Genco), and combined type of MO and Genco. Optimal conditions for Nash Equilibrium are derived in the form of market prices during the scheduling periods. Simulation results show the different ownership models produce different schedules of pumping and generating, which correspond to the objective of the scheduling owner of a pumped-storage hydro plant.