Demand response (DR) is envisioned as a promising solution to address the demand-supply mismatch issue in electric power systems. A new demand bidding model is considered in this paper to facilitate demand response trading in load curtailment form between the aggregator (buyer) and the large contract capacity customers (seller). Different types of customers with different load curtailment characteristics are considered in the demand bidding, leading to the formulation of a nonlinear optimization problem that is computationally expensive to solve. Delicate mechanisms are incorporated into the proposed purchase optimization scheme to reformulate the nonlinear programming problem into an equivalent linear model that can be solved efficiently. Simulation studies show that the proposed work is promising to minimize the total bidding purchase cost while satisfying the given load curtailment constraints that include the load curtailment and the load curtailment patterns of different customers.