In a fractured-vuggy carbonate reservoir (FVCR) are distributed many irregular natural fractures and cavities. They are the main oil/gas storage bodies. To stimulate such a reservoir, it is desired to connect the hydraulic fractures (HF) to them. To study the interaction mechanism between HFs and cavities in this paper, the natural fracture is modeled by the element partition method and the cavity is described by an ellipse equation at first. The surrounding fractured zone of a cavity is considered. Then the local and wellbore-nearby HF-cavity interactions are studied. It shows that the magnitude of in-situ stress has significant impact on their interaction due to the stress concentration surrounding a cavity. The higher in-situ stress leads to a stronger repulsion of a cavity to HF. The pore pressure and the surrounding fractured zone of a cavity can relieve the stress concentration, which facilitates the HF-cavity connection. The distributed natural fractures have the leading effect on HF direction when the in-situ stress difference is small. Next, the interaction between HF and cavity cluster is studied. It suggests that the injection mode has significant impact on the generation of fracture network. If the injection rate is adjusted properly, a complex fracture network can be generated. These findings help to deeply understand the HF-cavity interaction and provide valuable references for the HF treatment design in FVCR.