As one of the basic problems of smart grid, economic dispatch problem (EDP) has aroused extensive research interest with the expansion of network scale and the improvement of system complexity. The problem aims to ensure that the overall electricity demand and generating capacity are met while minimizing the overall power generation cost by optimizing the output power of individual generating units. In order to solve the EDP, a new distributed random sleep algorithm is proposed over time-varying unbalanced directed networks. The algorithm incorporates interfering noise in the information transmission process, which effectively protects privacy. Meanwhile, the random sleep strategy ensures that the algorithm has better computational efficiency. In addition, theoretical analysis is also provided to ensure the convergence and privacy of the proposed algorithm. Finally, the effectiveness of the algorithm is demonstrated by simulation experiments.