In this work, Fast Marching Method (FMM) has been suggested for Retinal blood vessels segmentation. FMM is an optimization technique; and the main advantage of the FMM is its ability to deal with branches and bifurcations without any additional computational cost. This advantage had been used in robotics to find the optimal path for the robot to move from the starting point to the goal with no collisions. Considereing the tree structure of blood vessel, I will use FMM to find the shortest bath between the optic disk and the blood vessels ends to draw the tree of the blood vessels.This method has been implemented using the M language in MATLAB R2016b. In this work local mathematical analysis has been implemented so that we can have an initial estimation of blood vessels distribution in an image in order to minimize the huge amount of noise included in retinal images and to make FMM implementing easier. FMM performance had been compared to other techniques used for retinal blood vessel detection like “Matched Filters”. The results showed that the FMM performance overcame some of those techniques and close to other high resolution methods. The FMM algorithm has been validated using the well-known “DRIVE” database and the resulting resolution ranged between 80% to 93% (depending on the noise amount in image) with iteration number between 500 to 1000 (according to the optic disk position in the image) with an average time of 0.57 seconds for each iteration which mean that the total running time is 5-10 minutes. FMM had also been validated using STARE data set and achieved a TPR of 90% for 700x605 STARE images in 15 minutes, and a TPR of 86% in 2.6 minutes when reducing image size to 350x303.