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Being an unsupervised learning, conventional k-means clustering algorithm suffers from the limitation which includes the dependence on prior knowledge to specify cluster parameter k and the sensitivity to initial centers. In this paper, we proposed a new k-means algorithm with meliorated initial centers, which obviates the needs of cluster parameter and can select effective initial centers skillfully. Firstly, it uses a cluster-validity-index based method to determine the optimal number of clusters k; then, computes the densities of the area where the data objects belongs to, and finds k data objects all of which are from high density area and the most far away from one another; finally, use these k data objects as the initial centers for further k-means clustering. The application of this new k-means algorithm to partition of diet structures shows its feasibility and validity.