To make full use of the flexible charging and discharging capabilities of the growing number of electric vehicles (EVs), a bidding strategy for EV aggregators to participate in a day-ahead electricity energy market is proposed in this work. The proposed bidding strategy is able to reduce the operating cost of the EV aggregators and to handle the uncertainties of day-ahead market prices properly at the same time. Agreements between the EV owners and the aggregators are discussed, and a hierarchical market structure is proposed. While assuming the aggregators as economic rational entities, the bidding strategy is established based on the market prices, extra battery charging/discharging costs and the expected profits. The bidding clearing system will display the current/temporal market clearance results of the day-ahead market before the final clearance, and hence the market participants can revise their bids and mitigate the risks, to some extent, of forecasted market price forecast errors. Numerical results with a modified IEEE 30-bus system have demonstrated the feasibility and effectiveness of the proposed strategy.