Acid fracturing is an important method of achieving high-efficiency economic development of carbonate reservoirs. The propagation of acid-etched fractures is affected significantly by geological discontinuities such as natural fractures and limestone caverns. Therefore, acid-etched fractures in carbonate reservoirs also differ greatly in morphology to those inhomogeneous reservoirs. However, no clear propagation mechanism has been available to describe and predict the propagation behavior of acid-etched fractures. In order to investigate the process, based on the extended finite element method, a set of acid-etched fracture propagation models for fracture-vuggy reservoirs, including mechanical, hydro and acid-rock reaction modules, were established. The effect of vuggy, natural fracture and acid on the initiation and propagation of induced fracture, the surface morphology of the acid-etched fractures, the effects of the number of perforation clusters, and natural limestone caverns, were considered. The calculated geometric size of the fracture was compared with the results based on the CGD (Christianovich-Geertsma-Daneshy model) model, for validating the reliability of the present model. The effects of the injection fracturing liquid type and the number of perforation clusters on fracture initiation position, propagation path, and surface morphology were evaluated. The calculation results also were compared with large-scale tri-axial physical experiment data. Finally, the fracture propagation behavior in rock samples containing natural fractures and limestone caverns was simulated in order to examine examining the effects of the limestone caverns with different sizes at different positions on the propagation path of acid-etched fractures. The interaction between induced fractures and limestone caverns was discussed. The induced fractures priority was given to activating natural fractures around the wellbore and extending along the natural fractures and tended to be deflected from the maximum horizontal principal stress direction due to the existence of caverns arrested fractures to a certain degree.