Virtual bidders place virtual offers/bids into day-ahead electricity market, and the cleared energy is settled at the price difference between day-ahead market and real-time market. With high volatility in the price difference, virtual bidders face great uncertainties and financial risks in their decision making. To date, few research has been devoted to bidding strategy of virtual bidders with the consideration of its impact on market prices. Therefore, this paper proposes a risk-constrained bi-level optimization model for virtual bidders bidding strategy. In this model, uncertainties related to the other market participants offers/bids and real-time market prices are modeled through scenarios. Financial risk associated with bidding decisions is modeled using conditional value-at-risk (CVaR) metric. By virtue of Karush-Kuhn-Tucker optimality conditions, strong duality theorem and Fortuny-Amat Transformation, the proposed bi-level model is converted to a single-level mixed integer linear programming model. A case study is presented to demonstrate the effectiveness of the proposed method.