Abstract: According to the traditional ROF model is prone to produce the staircase effect when repairring images, a new adaptive fractional TV repair algorithm is proposed. The algorithm uses the globality of fractional differential to extend the regular term of ROF repair model from first order differential to fractional differential, which effectively solves the staircase effect of traditional ROF model in repairing image. In addition, in order to maintain the edge of the repair image better, an adaptive edge instruction operator is designed on the fractional differential regular term. Because of the similarity between the model and the optimization model of the saddle point structure, the new model is solved by using the primitive dual algorithm based on the prerequisite, and the adaptive convolution filter function is used to control the diffusion of the new model repair. The experimental results show that compared with the traditional TV and TGV repair algorithm, the adaptive fractional TV repair algorithm proposed in this paper has better repair effect and can be better repaired for image damage such as patches, scratches and text.