The deployment of wind power plants equipped with energy storage systems is expected to mitigate the variability of wind power outputs. When these wind-storage units are encouraged to participate in the day-ahead (DA) electricity market as price-makers, their offering strategies will not only affect the market prices, but also be influenced by the bidding strategies of other market participants. In this context, a bi-level model considering strategic interactions between the wind-storage unit and other market participants in the DA market is proposed, aiming to investigate the impacts of the strategic interaction on the offering strategy and energy storage utilization of the wind-storage unit. At the upper-level, each market participant decides its offering strategy to maximize its own profit. At the lower level, the independent system operator (ISO) performs the DA market clearing to maximize social welfare. Then, the bi-level model is transformed into a single-level equilibrium problem and can be solved by using Karush–Kuhn–Tucker (KKT) conditions and nonlinear complementarity methods. Finally, the model’s reasonableness and effectiveness are verified through case studies. It is shown that the wind-storage unit’s strategic interaction with other market participants can help improve the utilization of energy storage and achieve higher profit.