In this paper, an efficient and robust level set method is presented to segment the images with intensity inhomogeneity. The multi-scale segmentation idea is incorporated into energy functional construction and a new Hermite differential operator is designed to numerically solve the level set evolution equation. Firstly, the circular shape window is used to define local region so as to approximate the image as well as intensity inhomogeneity. Then, multi-scale statistical analysis is performed on intensities of local circular regions centered in each pixel. So, the multi-scale local energy term can be constructed by fitting multi-scale approximation of inhomogeneity-free image in a piecewise constant way. To avoid the time-consuming re-initialization procedure, a new double-well potential function is adopted to construct the penalty energy term. Finally, the multi-scale segmentation is performed by minimizing the total energy functional. Here, a new differential operator based on Hermite polynomial interpolation is proposed to solve the minimization. The experiments and comparisons with three popular local region-based methods on images with different levels of intensity inhomogeneity have demonstrated the efficiency and robustness of the proposed method.