Although electricity market structures may be different from each country, they have a long-term forward market and a short-term spot market in general. Particularly, a bilateral contract transacted at a long-term forward market fixes the electricity price between a genco and a customer so that the customer can avoid risk due to price-spike in the spot market. The genco also can make an efficient risk-hedging strategy through the bilateral contract. In this paper, we propose a new mechanism for deriving the optimal bilateral contract price using game theory. This mechanism can make the customer reveal his true willingness to purchase so that an adequate bilateral contract price is derived.