Abstract: A novel variational denoising model is proposed based on the study of two-step model. By analysing the properties of new model, an efficient and fast numerical algorithm is introduced. There are two variables in the new model, so it is firstly turned into two simple submodels by using alternative minimization method in the new algorithm, and then the two submodels are solved using split Bregman method respectively. Experimental results show new algorithm not only has faster convergence rate, but also can alleviate the staircase effect and preserve the edge information better while removing noises.