Denoising is the representative task in hyperspectral image (HSI) processing. This letter proposes to produce a classification-driven HSI denoiser, which is capable of simultaneously reducing noise and preserving semantic-aware detail. The conditional neural adversarial network and multiple loss functions are introduced to produce visually pleasing images by enforcing an additional constraint that the denoised image must be indistinguishable from its corresponding ground-truth clean image. Experiments are performed on hyperspectral remote sensing images containing both the simulated hybrid noise and real noise. The results show that the proposed model outperforms many state-of-the-art denoising methods for HSIs.