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This paper tackles the challenging problem of hyperspectral (HS) image denoising. Unlike existing deep learning-based methods usually adopting complicated network architectures or empirically stacking off-the-shelf modules to pursue performance improvement, we focus on the efficient and effective feature extraction manner for capturing the high-dimensional characteristics of HS images. To be specific, based on the theoretical analysis that increasing the rank of the matrix formed by the unfolded convolutional kernels can promote feature diversity, we propose rank-enhanced low-dimensional convolution set (Re-ConvSet), which separately performs 1-D convolution along the three dimensions of an HS image side-by-side, and then aggregates the resulting spatial-spectral embeddings via a learnable compression layer. Re-ConvSet not only learns the diverse spatial-spectral features of HS images, but also reduces the parameters and complexity of the network. We then incorporate Re-ConvSet into the widely-used U-Net architecture to construct an HS image denoising method. Surprisingly, we observe such a concise framework outperforms the most recent method to a large extent in terms of quantitative metrics, visual results, and efficiency. We believe our work may shed light on deep learning-based HS image processing and analysis.