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The global k-means algorithm is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure from suitable initial positions, and employs k-means to minimize the sum of the intra-cluster variances. However the global k-means algorithm sometimes results singleton clusters and the initial positions sometimes are bad, after a bad initialization, poor local optimal can be easily obtained by k-means algorithm. In this paper, we modified the global k-means algorithm to eliminate the singleton clusters at first, and then we apply MinMax k-means clustering error method to global k-means algorithm to overcome the effect of bad initialization, proposed the global Minmax k-means algorithm. The proposed clustering method is tested on some popular data sets and compared to the k-means algorithm, the global k-means algorithm and the MinMax k-means algorithm. The experiment results show our proposed algorithm outperforms other algorithms mentioned in the paper. [ABSTRACT FROM AUTHOR]