A dual phase titanium alloy of the Ti-6Al-4V type was tested at a slow strain rate under uniaxial tension in ambient environment. The fracture was found to be largely transgranular, but the fracture initiation was observed to occur from grain boundary microcracks. A fracture model has been proposed to explain the interesting phenomenon. According to the model, the fracture begins with microcrack initiation at α grain boundaries (especially the triple points) or α/β interfaces. As the applied load increases, sliding occurs in those grain boundaries whose orientation coincides with that of the maximum shear stress. The titanium alloy has a very low work hardening rate; therefore, above a certain stress level, strain localisation occurs to form concentrated shear band at roughly 45 degrees to the loading axis, leading to the final transgranular fracture by shear.