Both the strength and its variance of carbon fibers depend on the worst flaw that exists in the fiber, or more exactly speaking, on the structure of the "fiber weak link" (FWL). To better understand the strength-structure relationship, the fracture-ends morphologies were examined by the scanning electron microscope (SEM). The weak links of carbon fibers were divided into three groups according to its tensile strength, and the effect of the carbon FWLs on the strength variance was also discussed. The observation by SEM, the analysis on fiber tensile properties, and the corresponding discussion of the two sorts of results indicate that both Surface flaw and the incompact structure decrease the strength of carbon fiber and enlarge the strength variance of carbon fiber. The modulus seems to influence the strength of carbon fibers too. It is also confirmed that not only the size of the fracture mirror but also the ratio of the size of the mirror to the fracture surface area (not cross section area) is important for judging the strength of brittle fibers. (C) 2008 Wiley Periodicals, Inc. J Appl Polym Sci 110: 3778-3784, 2008