Accurate description of vasculature structure plays an important role in many clinical applications. The purpose of this paper is to provide a new method based on geometric flows for vessel extraction from magnetic resonance angiography (MRA) images. This method is based on recent surface evolution work which models the object boundary as a manifold that evolves to maximize the rate of increase of flux of an appropriate vector field, and the geodesic active contour is used for regularization. In addition, to improve the insufficient of geometrical description of blood vessel structure, the centerlines of the vascular structure are regarded as space curves, and a tube of small radius around the centerline can be regarded as a distance function. Furthermore, the method uses the level set method to represent the surface evolution as it is intrinsic and topologically flexible. Results on cases demonstrate the effectiveness and accuracy of the approach comparing with the maximum intensity projection (MIP) and other methods.