How to identify influential nodes in social networks is of theoretical significance, which relates to how to prevent epidemic spreading or cascading failure, how to accelerate information diffusion, and so on. In this Letter, we make an attempt to find \emph{effective multiple spreaders} in complex networks by generalizing the idea of the coloring problem in graph theory to complex networks. In our method, each node in a network is colored by one kind of color and nodes with the same color are sorted into an independent set. Then, for a given centrality index, the nodes with the highest centrality in an independent set are chosen as multiple spreaders. Comparing this approach with the traditional method, in which nodes with the highest centrality from the \emph{entire} network perspective are chosen, we find that our method is more effective in accelerating the spreading process and maximizing the spreading coverage than the traditional method, no matter in network models or in real social networks. Meanwhile, the low computational complexity of the coloring algorithm guarantees the potential applications of our method.