A new level set method is proposed to segment medical images by introducing intensity inhomogeneity and a double well potential function. First of all, an adaptive weighted median filter (AWMF) is used to define the region with respect to intensity inhomogeneity. Then, the analysis is performed by incorporating an energy function with intensity inhomogeneity-free images. Thereafter a new double well potential function is introduced that reduces the computational time. Finally, segmentation is performed on medical images by minimizing the overall energy function. The experimental results show the robustness of the proposed method in comparison to the existing methods in terms of computational time and Jaccard Index (JI).