Economic dispatch is a critical problem in operation of power grids. A consensus-based algorithm was recently proposed to solve the economic dispatch problem in a distributed manner. In this paper, we propose a novel secure scheme for the consensus-based economic dispatch algorithm using the Paillier cryptosystem. This secure scheme ensures that not only the network transmitted information is protected from external malicious party but also the privacy information of each node remains intact. The proposed secure scheme has two features. First, it relies on the solution to the so-called structural consensus problem with time-varying network weights. Second, it contains a strategy for transmitting encrypted information and generating network weights with randomness, as well as treatment of the practical issues like quantization error and computation overflow/underflow. The performance in terms of cost optimization and privacy-preserving is verified by rigorous theoretical analysis and numerical simulation.