This paper describes a creep rupture model that takes into account the interfacial debonding and its propagation around broken fibers in unidirectional fiber-reinforced polymers. The interfacial debonding is accompanied by fiber breaks under a longitudinal tensile load, and it causes the material property to decrease with increase of the interfacial debonding length. Also, there is a interaction between probability of fiber break and the growth of the interfacial debonding, eventually, the rate of the decrease of material properties is exponentially. In this study, the probability of the fiber break is formulated as a function of stress recovery length that has a time-dependency and the creep rupture strain is predicted as a function of the increase rate of the stress recovery length. Moreover, the creep behavior is predicted by using compliance component of the matrix as a function of time. It is assumed that when the composite strain reaches the time-dependent material rupture strain, the composite fails in creep rupture.