Removing stripe noise is a fundamental task in remote sensing image processing, which is of great significance for improving image quality and subsequent applications. In this paper, an adaptive strip noise removal model is proposed with the spatial characteristics. Firstly, an adaptive weight function is constructed using local absolute differences to adaptively control the constraint intensity of the penalty term at different pixel points in the adaptive strip noise removal model. Secondly, L1 norm is used to constrain the local smoothness along the direction of the strip, maintaining the obvious smoothness characteristics of the strip noise in its extension direction, while L2 norm is used to restrict the image grayscale. Finally, the extended split Bregman iteration method and alternating minimization method is used to optimize the proposed image destriping model. Extensive experiments on both the synthetic and real remote sensing images validate that the proposed model can effectively remove the stripe noise and preserve more fine scale details.