Region scalable fitting (RSF) active contour model has limitation in segmenting image with weak texture and weak edge, troubled by inclining to local minimum and slow evolution speed. Aiming at the problem, this paper proposes a new active contour model with fractional order derivative operator capable of adjusting degree adaptively. Firstly, the global Grünwald-Letnikov (G-L) fractional gradient is integrated with the RSF model, which can strengthen the gradient of regions with intensity inhomogeneity and weak texture. As a result, both the robustness to initial location of evolution curve and efficiency of image segmentation are improved. Secondly, the Gaussian kernel function in local fitting term is replaced by bilateral filtering, and the blurred boundary caused by Gaussian kernel function in the process of curve evolution can be tackled. Lastly, an adaptive fractional order mathematical model is constructed based on the gradient magnitude and information entropy of image, therefore the optimal fractional degree is adjusted adaptively. Theoretical analysis and experimental results show that the proposed algorithm is capable of segmenting images with intensity inhomogeneity and weak texture. And the optimal degree of fractional order derivative operator can be calculated adaptively. Furthermore, the presented method is capable of avoiding falling into local optimum, thus the efficiency of image segmentation can be improved.