Flexible loads, most of which are on/off appliances, are playing an important role in keeping the balance between power generation and demand. In this paper, a distributed consensus-based control strategy is proposed for the economic load dispatch in the frequency regulation. In order to avoid the complexity caused by the discrete cost characteristics, the continuous cost function of each user is fitted by the least squares method in advance. To minimize the overall load dispatching costs during the frequency regulation, Incremental Cost Consensus (ICC) algorithm is proposed in the load control. The economic load dispatch is realized through the convergence of the Incremental Cost (IC) of users. Case studies are provided to verify the effectiveness of the proposed method, with comparisons of different discretization methods.