Active contour models have been extensively applied to image processing and computer vision. In this paper, we present a novel adaptive method combines the advantages of the SBGFRLS model and GAC model. It can segment images in presence of low contrast, noise, weak edge and intensity inhomogeneity. Firstly, a region term is introduced. It can be seen as the global information part of our model and it is available for images with low gray values. Secondly, Legendre polynomials are employed in the local statistical information part to approximate region intensity and then our model can deal with images with intensity inhomogeneity or weak edges. Thirdly, a correction term is selected to improve the performance of curve evolution. Synthetic and real images are tested and Dice similarity coefficients of different models are compared in this paper. Experiments show that our model can obtain better segmental results.