An anastomosis system includes a base, two rings, and a blood vessel-leading unit. A first blood vessel can be inserted in and attached to the first ring by the blood vessel-leading unit. A second blood vessel can be inserted in and attached to the second ring by the blood vessel-leading unit. The first ring is placed on a ring-guiding base in a specific manner. The second ring is placed on the ring-guiding base in a movable and rotatable manner to assure the alignment of the blood vessels in both axial and angular directions. The two rings are interconnected by at least one snap-on mechanism or buckle so that the interconnection of the rings is efficient.