In order to design new fatigue-resistant composites, the underlying fatigue damage mechanisms must be characterized and the controlling microstructural properties should be identified. The fatigue-damage mechanisms of a unidirectional carbon fiber-reinforced epoxy has been studied under tension-tension loading. A ubiquitous form of damage was one or a few planar fiber breaks from which debonds or shear yield zones grew in the longitudinal direction during fatigue cycling. This leads to a change in stress profile of the neighboring fibers, and an increase in failure probability of these fibers. The breakage of fibers in the composite is controlled by the fiber strength distribution. The interaction between the fiber strength distribution and debond propagation leading to further fiber breakage was investigated by a numerical simulation. It was found that a wider distribution of fiber strength and a higher debond rate lead to more distributed damage and a higher fracture toughness. Implications to fatigue life behavior are discussed, with reference to constituent microstructure.