The effects of stress ratio on high-cycle fatigue (HCF) and very-high-cycle fatigue (VHCF) behavior of a Ti-6Al-4V alloy were systematically investigated in this paper. Fatigue tests with ultrasonic frequency (20 kHz) were performed on specimens of a bimodal Ti-6Al-4V alloy with stress ratios of -1, -0.5, -0.1, 0.1 and 0.5. Three types of crack initiation mode were observed on the fracture surfaces of the specimens that failed in the HCF and the VHCF regimes, which were explicitly classified as surface-without-facets, surface-with-facets and interior-with-facets. With the increase of stress ratio from 1 to 0.5, the number of specimens for surface-without-facets decreased, that for surface-with-facets increased, and that for interior-with-facets increased first and then decreased. For the failure types of surface-with-facets and interior-with-facets, the fatigue strength decreased sharply in the VHCF regime, and the S-N curve switched from an asymptote shape to a duplex shape. Then, a new model based on Poisson defect distribution was proposed to describe the effects of stress ratio on the occurrence of different failure types, i.e., the competition of alternative failure types. The observations also showed that there is a rough area at the crack initiation region for interior initiation cases, and the values of the stress intensity factor range for the rough area are within a small range, with the mean value being close to the threshold for the crack starting to grow in vacuum environment of the alloy. The estimated value of plastic zone size at the periphery of rough area is close to the average diameter of the primary cc grains of the alloy.