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Hyperspectral image (HSI) classification has become one of the most significant tasks in the field of hyperspectral analysis. However, classifying each pixel in HSI accurately is challenging due to the curse of dimensionality and limited training samples. In this paper, we present an HSI classification architecture called camera spectral response network (CSR-Net), which can learn the optimal camera spectral response (CSR) function for HSI classification problems and effectively reduce the spectral dimensions of HSI. Specifically, we design a convolutional layer to simulate the capturing process of cameras, which learns the optimal CSR function for HSI classification. Then, spectral and spatial features are further extracted by spectral and spatial attention modules. On one hand, the learned CSR can be implemented physically and directly used to capture scenes, which makes the image acquisition process more convenient. On the other hand, compared with ordinary HSIs, we only need images with far fewer bands, without sacrificing the classification precision and avoiding the curse of dimensionality. The experimental results of four popular public hyperspectral datasets show that our method, with only a few image bands, outperforms state-of-the-art HSI classification methods which utilize the full spectral bands of images.