Edge detection is a crucial method for the location and quantity estimation of oil slick when oil spills on the sea. In this paper, we present a robust active contour edge detection algorithm for oil spill remote sensing images. In the proposed algorithm, we define a local Gaussian data fitting energy term with spatially varying means and variances, and this data fitting energy term is introduced into a global minimization active contour (GMAC) framework. The energy function minimization is achieved fast by a dual formulation of the weighted total variation norm. The proposed algorithm avoids the existence of local minima, does not require the definition of initial contour, and is robust to weak boundaries, high noise and severe intensity inhomogeneity exiting in oil slick remote sensing images. Furthermore, the edge detection of oil slick and the correction of intensity inhomogeneity are simultaneously achieved via the proposed algorithm. The experiment results have shown that a superior performance of proposed algorithm over state-of-the-art edge detection algorithms. In addition, the proposed algorithm can also deal with the special images with the object and background of the same intensity means but different variances.