An optical fiber cleaving device includes an auxiliary support section movably disposed on a base section independently from a blade section and a pusher section. The auxiliary support section can be selectively disposed at the operable position for supporting an unsheathed optical fiber in cooperation with a pair of clamp sections. The auxiliary support section is constituted by a thin plate member having fiber support faces locally located between the clamp sections at the operable position and a relief area formed adjacent to the fiber support faces. The fiber support faces come in contact with the portions of a local length of the unsheathed optical fiber extending between the clamp sections, the local length being located away from the fiber cleaving position, and the relief area is so arranged as to avoid the contact with a portion of a second local length of the unsheathed optical fiber, located at the fiber cleaving position. The cleaving device can provide highly accurate cleaving for optical fibers having different fiber structures without changing the preset conditions for the clamp sections.