In order to solve the problem of complicated calculation and frequent human intervention, a new method for extracting the centerline of blood vessel based on magnetic resonance angiography (MRA) is proposed in this paper. First of all, according to the different diameter of blood vessels, the multi-scale filtering algorithm is utilized for enhancing the different scales of blood vessels by Hessian matrix. The discriminant function is established based on the gray distribution of the blood vessel and the differential operator, and then the initial position and the orientation direction of the seed point are obtained. Secondly, the new ridge point and tracing direction are optimized in the local arc length range of the initial direction to ensure that the correct ridge point position can be obtained even with large error interference. Finally, we eliminate pseudo-centerlines that do not satisfy the initial conditions and get the final centerline of the vessel to be extracted. The experimental results show that this method can automatically extract the blood vessel centerline from the MRA images without manual intervention.