This paper presents a sequential solution method to discover efficient trades in an electricity market model. The market model represents deregulated electricity market consisting of four types of participants: independent power producers, retailers, public utilities, and consumers. Our model is based on graph theory, and the market participants are denoted by a network composes of three types of agents including sellers, buyers, and traders. The market participants have different capacity and demand of electricity from each other, and each electricity trade should satisfy the capacity and demand. Our sequential solution method can discover efficient electricity trades satisfying the constraints regarding capacity and demand by utilizing network flow. Simulation results demonstrate the efficiency of electricity trades determined by our method by examining social welfare, which is the total of payoffs of all market participants. Furthermore, the simulation results also indicate the allocation of payoff to each market participant.