Stripe noise disturbs the quality of hyperspectral images (HSIs), and decreases the precision and robustness of the downstream data analysis. After analyzing the characteristics of stripe noise of HSIs, that is, stripe noise is directional and noise intensities vary in each band, a new destriping method based on the adaptive unidirectional variation is proposed. On the basis of the unidirectional variation model, an energy function with a coupling term is constructed, which is then optimized iteratively with the gradient descent method. Experimental results demonstrate that the mean equivalent number of looks of real HSIs improves from 26.49 to 85.61, and the mean improvement factor of radiometric quality increases to 9.34 dB. Compared with the conventional methods, the proposed method can adapt to the spectrally varying stripe noise intensities, and is capable of removing stripe noise without loss of detail information and improving the image quality.