Abstract: A piecewise variational decomposition model is proposed to reduce staircase appeared in structure component obtained by TV based models and precisely extract oscillatory component.The image domain is clustered into 2 subregions which have distinct characteristic.The image function supported on smooth region is decomposed by fix-boundary Mumford-Shah model for ameliorating staircase.While image function supported on transition region is decomposed by(BV,G) decomposition for oscillation precise extraction.And then,the conditions of existence of nontrivial solution for this model are discussed.At last,an alternating iterative algorithm combined with gradient descent method and finite difference scheme is used to solve this model.The experimental results and comparisons to TV model are presented to validate the proposed new model.