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Feature selection, which aims to select the most informative feature subset, has been playing a critical role in dimension reduction. In this paper, a novel unsupervised feature selection algorithm called the inner product regularized nonnegative self-representation (IRNSR) is designed for image classification and clustering. In the IRNSR algorithm, first, each feature in high-dimensional data is represented by a linear combination of other features. Then, the inner product regularized loss function is introduced into the objective function with the aim of reducing the correlation and redundancy among the selected features. More importantly, a simple yet efficient iterative update optimization algorithm is accordingly designed to solve the objective function. The convergence behavior of the proposed optimization algorithm is also analyzed. Comparative experiments on six image databases indicate that the proposed IRNSR algorithm is effective and efficient.