Higher degree total variation (HDTV) denoising algorithm is the fully separable L1 norm of the image directional derivatives. The usage of this denoising algorithm is seen to effectively denoise images while preserving details and features in the image. However, the traditional HDTV method has the disadvantage of low computation speed due to the comparatively high computational complexity. An augmented Lagrangian multiplier based fast HDTV image denoising algorithm is introduced. Firstly, the Huber function is used to reformulate the HDTV optimization function. Secondly, by introducing the auxiliary variable and the Lagrangian multiplier, the original problem is converted into two subproblems which can be solved using the alternating minimization method efficiently. The results demonstrate that compared with the traditional algorithm, the proposed algorithm is able to obtain ten times speedup. Besides, the proposed algorithm is able to better preserve the image details and edges information.