The precise annotation of vessel is desired in computer-assisted systems to help surgeons identify each vessel branch. A method has been reported that annotates vessels on volume rendered images by rendering their names on them using a two-pass rendering process. In the reported method, however, cylinder surface models of the vessels should be generated for writing vessels names. In fact, vessels are not actual cylinders, so the surfaces of the vessels cannot be simulated by such models accurately. This paper presents a model-free method for annotating vessels on volume rendered images by rendering their names on them using the two-pass rendering process: surface rendering and volume rendering. In the surface rendering process, docking points of vessel names are estimated by using such properties as centerlines, running directions, and vessel regions which are obtained in preprocess. Then the vessel names are pasted on the vessel surfaces at the docking points. In the volume rendering process, volume image is rendered using a fast volume rendering algorithm with depth buffer of image rendered in the surface rendering process. Finally, those rendered images are blended into an image as a result. In order to confirm the proposed method, a visualizing system for the automated annotation of abdominal arteries is performed. The experimental results show that vessel names can be drawn on the corresponding vessel in the volume rendered images correctly. The proposed method has enormous potential to be adopted to annotate other organs which cannot be modeled using regular geometrical surface.