Hyperspectral Images (HSIs) demonstrates significant application value in various fields such as facial recognition, agricultural monitoring, medical diagnosis, and geological exploration due to its rich spectral information. However, HSIs are susceptible to noise contamination during acquisition, which limits its practical effectiveness. Generally, HSI denoising methods are divided into two categories: traditional prior-based methods and deep learning-based methods. Traditional methods rely on handcrafted priors, which may be insufficient for all scenarios, while deep learning methods often ignore these priorities and introduce redundancy. Both have practical limitations. To address this, we propose the Adaptive Spectral Filter Sparse Transformer (ASFST). It integrates three modules: Adaptive Spectral Filter (ASF), Adaptive Gated Sparse Self-Attention (AGSSA), and Spectral Amplification Attention (SAA). ASF combines traditional filters for better denoising, AGSSA reduces redundancy via a gating mechanism while preserving details, and SAA enhances spectral channel perception. Experimental results demonstrate that ASFST achieves state-of-the-art performance in HSI denoising tasks.