Social energy efficiency has posed a new challenge for the operation and development of the power market. Three solving methods， i.e. bidding by energy cost， by energy-embedded price and by energy-consumption-constraint， are discussed. The energy-consumption-constraint bidding mode is proposed and the bidding model and algorithm are presented based on the yearly or monthly medium-and long-term power market. A simple numerical analysis is made with RTS data， the results of which show that the energy-consumption-constraint bidding mode is effective in improving energy efficiency and market efficiency， while also a feasible method for the actual power market.