Abstract: In this paper, a mathematical model is firstly built for economic dispatch of a hybrid resource system consisting of power plants, water plants, and coproduction plants. For this kind of optimization model considering the complex relation of the power and water in production, a continuous-time distributed algorithm is proposed to find the optimal solution of the economic dispatch problem. The convergence analysis shows that the trajectories converge to the optimal solution regardless of the initial allocation, avoiding the consideration of the initial procedure in detail. Moreover, applying the proposed algorithm, the plants no longer need to exchange the gradient information of the cost functions with their neighbors, which can protect the privacy of the plants. Finally, a numerical example is provided to demonstrate the performance and effectiveness of the proposed algorithm for the energy-water nexus.