Intensity inhomogeneity often occurs in natural and medical images, and it is hard to accurately segment intensity inhomogeneous images because most popular segmentation models are based on intensity homogeneous images. In this paper, we propose a novel level set-based segmentation model which integrates adaptive gradient weighted information (AGWI) and local region information to handle intensity inhomogeneous images. By employing AGWI in local regions, we combine the edge information and region information. Furthermore, the complementation of edge information and region information will enhance the robustness and effectiveness of our method. Finally, we compare our model with the local Chan-Vese (LCV) model and local intensity clustering (LIC) model. Some experiments on synthetic and nature images will be shown to demonstrate the efficiency and robustness of our method.