The carbonate reservoir has characteristics of strong heterogeneity and developed natural fractures，and it is always treated by acidizing to remove pollution near the wellbore area. The existence of natural fractures makes heterogeneity of carbonate reservoir stronger，which would affect the wormhole development significantly in acidizing process. Only few research on wormhole developed in carbonate rocks fracture with natural has been reported，while current studies mainly focus on the rule of wormhole growing in carbonate rock matrix. The effect of natural fracture length，natural fracture density and direction on wormhole pattern and acid injection volume for breakthrough were analyzed by a radial dual-scale continuum model based on equivalent theory. The results show that the developed wormholes in injection side without fractures are restrained and the acid volume for breakthrough decreases with an increasing length of fractures parallel to acid injection direction. The rise of natural fracture number leads to fewer developed wormhole and lower injection pressure in other directions of inlet，while the acid injection volume for breakthrough are dependent on physical property of oil reservoirs before natural fractures. The natural fractures perpendicular to acid injection direction can only change the wormhole pattern nearby，and it needs more acid to inject to achieve breakthrough of wormhole.