By introducing a novel spatial-spectral domain mixing prior, this paper establishes a maximum a posterior (MAP) framework for hyperspectral images (HSIs) denoising. The proposed mixing prior takes advantage of different properties of HSI in the spatial and spectral domain. Furthermore, we proposed a spatially adaptive weighted prior combining smoothing prior and discontinuity-preserving prior in the spectral domain. The weights can be defined as a function of the spectral discontinuity measure (DM). For minimizing the objective function, a half-quadratic optimization algorithm is used. The experimental results illustrate that our proposed model can get a higher signal-to-noise ratio (SNR) than using only smoothing prior or discontinuity-preserving prior.