In this paper, we propose a new interactive retinal vessels extraction method with anisotropic fast marching (AFM) based on the observation that one vessel may have the property of local intensities consistency. Our goal is to extract both the centrelines and boundaries between two given points. The proposed method consists of two stages: the first stage aims to finding the vessel centrelines using AFM and local intensities consistency roughly, while the second stage is to refine the centrelines from the previous stage using constrained Riemannian metric based AFM, and get the boundaries of the vessels simultaneously. Experiments show that results of our method outperform the classical minimal path method [1].