A fusion splicing apparatus includes discharge electrodes 13 and 15 to discharge-heat and fusion-splice end faces 5a and 7a of optical fibers 1 and 3, fiber holders 17 and 19 to hold the optical fibers 1 and 3, V-groove blocks 21 and 23 to receive, position, and fix parts of the optical fibers 1 and 3 on the end face sides of the fiber holders 17 and 19, V-groove-block moving mechanisms 33 and 35 to move the V-groove blocks 21 and 23 so as to shift an axial center of the optical fibers 1 and 3 from a straight line between the discharge electrodes 13 and 15, and holder moving mechanisms 37 and 39 to move the fiber holders 17 and 19 so as to shift the axial center of the optical fibers 1 and 3 from the straight line between the discharge electrodes 13 and 15.