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Resulting from the mismatch of constraints between unit commitment and economic dispatch, constraint relaxation is commonly utilized in market-clearing models to remain a feasible solution. If the constraint relaxation is active, price spikes may incur. Previous work has proposed a pricing method to handle the issue, which takes the prices as the decision variables and formulates the relationship of incentive compatibility. However, the previous work can be enhanced in two parts: (1) the multi-period influence is not incorporated, which is not applicable for the day-ahead market; (2) the market surplus of the previous method is irrationally large. To resolve the issues, this paper proposes a multi-interval pricing method based on bi-level optimization. The market surplus constraint is included in the proposed pricing model and the multi-interval incentive-compatibility constraint of each generator is formulated. To solve the pricing model reliably, the bi-level optimization model is transferred into a mixed-integer linear programming problem based on KKT conditions. The effectiveness of the proposed method is verified in the IEEE 30-bus system.