An apparatus to cleave an optical fiber includes a base plate, a jig slidably provided on the base plate and holding the optical fiber, a stripper provided near the jig, and including a hot plate heating a sheath of the optical fiber, a sheath cutter cleaving the sheath of the optical fiber to be stripped, a cleaning part cleaning the optical fiber after the sheath of the optical fiber is stripped according as the jig slides, and a cleaver provided on the base plate and cleaving the optical fiber whose sheath is stripped by the stripper. With this configuration, an apparatus is provided to cleave an optical fiber, in which stripping and cleaning processes are simultaneously performed in a stripper, so that the whole process of cleaving the optical fiber is decreased, and the structure of the apparatus is simplified without the conventional cleaning part.