Some recent research reveals that a topological structure in meta-heuristic algorithms can effectively enhance the interaction of population, and thus improve their performance. Inspired by it, we creatively investigate the effectiveness of using a scale-free network in differential evolution methods, and propose a scale-free network-based differential evolution method. The novelties of this paper include a scale-free network-based population structure and a new mutation operator designed to fully utilize the neighborhood information provided by a scale-free structure. The elite individuals and population at the latest generation are both employed to guide a global optimization process. In this manner, the proposed algorithm owns balanced exploration and exploitation capabilities to alleviate the drawbacks of premature convergence. Experimental and statistical analyses are performed on the CEC'17 benchmark function suite and three real world problems. Results demonstrate its superior effectiveness and efficiency in comparison with its competitive peers.