A numerical simulation was conducted to discuss the influence of fiber/matrix interfacial properties on strength and fracture property of unidirectional carbon fiber reinforced plastic (CFRP). The simulation addressed the matrix crack with a continuum damage mechanics model and the fiber break with the Weibull model. Based on these assumptions, the simulation was conducted with a finite element unit cell model, which can include the periodicity of the model. To investigate the influence of fiber/matrix interfacial properties on the composite strength, we utilized a cohesive zone model (CZM), considering interfacial strength and fracture toughness. In this paper, the stress distribution around a fiber break and the strength of the unidirectional CFRP were analyzed when the interfacial strength and/or fracture toughness were varied. The simulated results showed that the strength of the unidirectional CFRP increases with an increase of the interfacial properties. It was also found that the relationship between composite strength and interfacial strength is characterized by four different fracture modes.