Abstract The increasingly complex modern energy network arouses the need of flexible and dependable approaches to solve the economic dispatch problem (EDP) in the smart grids. Toward this end, this paper develops a fresh distributed algorithm with constant step-size, which aims to schedule the power generation among generators by complying with individual generation capacity limits to satisfy the total load demand at the minimized cost. The convergence of the proposed algorithm is analyzed through utilizing the Lyapunov method and the spectral decomposition technique. When the selected constant step-size is smaller than a specifically provided upper bound, the theoretical analysis demonstrates that the proposed algorithm can linearly achieve the optimal solution of the EDP under the smooth and strongly convex assumption on generation cost functions. In particular, the linear convergence rate of the proposed algorithm is tunable, and a relationship among the linear convergence rate, generation cost functions, network topology, weight matrix and constant step-size is established. The availability of the proposed algorithm is verified through simulation experiments.