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This paper proposes an iterative sparse representation-based algorithm for voxel selection in functional magnetic resonance imaging (fMRI) data. The output of the algorithm is a sparse weight vector, of which the magnitude of each entry represents the significance of its corresponding voxel with respect to mental tasks or stimulus. To demonstrate the validity of our algorithm and illustrate its application, we apply this algorithm to the Pittsburgh Brain Activity Interpretation Competition (PBAIC) 2007 fMRI data set for selecting the voxels which are the most relevant to the tasks of the subjects. Compared with three baseline methods, general linear model (GLM)-based statistical parametric mapping (SPM), correlation method and mutual information method, our method shows satisfactory performance for voxel selection.