Image can be decomposed into homogenous components u and oscillatory components v by using variational methods. However the solution of traditional variational methods has contrast loss and staircasing effect. Now we propose a local adaptive variational decomposition method based on L1. Using L1-norm as the fidelity term

we can get the solution which preserves the edges of original images and the contrast invariant. At the same time

the adaptive function which we induced here can reduce the staircasing effect on homogenous component u. Numerical results are presented

showing that the new method works better on several various types of images for image decomposition and denoising than traditional methods.