Abstract: This study firstly analyzes the model for Poisson noise removal by Le et al. (2007) from the view of calculus of variations, and gets a box constraint of the solution to the model. Then by incorporating the Alternating Direction Method of Multipliers (ADMM) algorithm, a fast total variation algorithm based on box constraint is proposed to solve the above model numerically, and the convergence of the fast algorithm is proved. Finally, experimental results are reported to demonstrate the feasibility and effectiveness of this algorithm.