In this paper, the failure behavior of SiC fiber-reinforced Ti-6Al-4V matrix composite (SiCf/Ti) under longitudinal loads was studied experimentally and theoretically. Experimental results show that the interface of SiCf/Ti composite is continuous and integral. Through SEM observations, it was found that transverse matrix cracks initiated from the debonding region of the interface. A three-dimensional representative volume element was developed to simulate the failure process of SiCf/Ti-6Al-4V composite. A continuum cohesive zone model is employed to describe the debonding behavior at the interface, compared with a discrete one. More accurate simulated results were obtained by a continuum cohesive zone model, corresponding to experimental results. The transverse cracking behavior of the matrix was simulated. The stress–strain curves predicted by the continuum cohesive zone model show a good agreement with the experimental results. The fiber volume fraction, interface strength and interface toughness are investigated to exhibit their influences upon the longitudinal mechanical characteristics of SiCf/Ti-6Al-4V composite.