Hyperspectral images (HSIs) are generally susceptible to various noise, such as Gaussian and stripe noise. Recently, numerous denoising algorithms have been proposed to recover the HSIs. However, those approaches cannot use spectral information efficiently and suffer from the weakness of stripe noise removal. Here, we propose a tensor decomposition method with two different constraints to remove the mixed noise from HSIs. For a HSI cube, we first employ the tensor singular value decomposition (t-SVD) to effectively preserve the low-rank information of HSIs. Considering the continuity property of HSIs spectra, we design a simple smoothness constraint by using Tikhonov regularization for tensor decomposition to enhance the denoising performance. Moreover, we also design a new unidirectional total variation (TV) constraint to filter the stripe noise from HSIs. This strategy will achieve better performance for preserving images details than original TV models. The developed method is evaluated on both synthetic and real noisy HSIs, and shows the favorable results.