Denoising is one of the fundamental pre-processing tasks in image processing that improves the quality of the information in the image. Processing of hyperspectral images requires high computational power and time. In this paper, a denoising technique based on least square weighted regularization in the spectral domain is proposed. The proposed technique is experimented on standard hyperspectral datasets and also, the performance of the proposed least square denoising in spectral domain is compared with least square weighted regularization in the spatial domain and total variation based denoising method. The obtained results in terms of computational time, Signal-to-Noise Ratio calculations and visual interpretation depicts that the proposed technique performs comparably better than the existing methods such as least square and total variation based hyperspectral image denoising.