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In this paper, a novel conjectured supply function equilibrium (CSFE) based model is presented for simulating strategic interactions among generation companies (GenCos) in an electricity market under incomplete information. The model is derived theoretically from the well-acknowledged supply function equilibrium theory, and a general supply function for a GenCo is obtained based on its conjectural variation of the rivals' accumulated response to a change in the market price. The CSFE is a general and flexible model for simulating strategic behaviors of GenCos in an electricity market with inelastic demand. Supply functions will be linear when GenCos hold constant conjectures, and a unique equilibrium exists when linear supply functions are provided to the market. Finally, the IEEE 30-bus system is used to show the essential features of the proposed model.