Carbonates with different reservoir space types have different hydraulic fracture propagation modes. But there is poor understanding of the fracture characteristics of fractured and fracture-cavity carbonates. It is difficult to effectively increase the complexity of fractures and increase the recovery rate under acid fracturing conditions. Fractured and fracture-cavity type    carbonate rocks were used to implement laboratory true triaxial acid fracturing, and a 3D profile scanning method was applied to observe the roughness of the fracture surface. The geometry of hydraulic fractures, fracture propagation, and characteristics of the pump-pressure curves were analyzed. Experimental results have shown: (1) Whether it was fracture-cavity type or fractured type carbonate, the natural weak structure (fracture or holes) in the matrix had played a positive role in inducing the extension of artificial fractures. The different natural weak structures led to different fracturing: fracture-cavity carbonate was more likely to form single fractures; fractured type carbonate was more likely to form complex cross-type fractures. (2) Fractured-cavity carbonate rocks had lower fracture pressure and secondary fluctuation emerged in the curve, which was greatly affected by the cavities. Fractured carbonate rocks had higher fracture pressure, only one fluctuation occurred, and the pressure dropped faster. (3) The region acid worked on was different. In fracture carbonate, acid dominantly migrated around the wellhead with slight etching in other regions, and leaked along the cracks. Conversely, in fracture-cavity carbonate, acid migrated across a wider area: the section near the wellbore had the deepest etching degree and the best weakening effect, as the distance from the wellbore increased, the weakening effect gradually reduced. (4) Pump-pressure curves under the conditions of slick water fracturing, acid fluid fracturing and slick water fracturing after acid etch were compared. For carbonate, acid fracturing had the most obvious effect on reducing fracture pressure, which was better than acid soaking treatment, while slick water fracturing had the highest fracture pressure. Using acid immersion treatment, acid would erode the open-hole section, which reduced rock strength. Using acid hydraulic fracturing, the acid fluid mainly interacted with carbonate rocks along the fracture path, when weakening effect was more obvious than in immersion treatment. For the fracturing of carbonate with different reservoir types, even using same construction parameters and under same in-situ stress conditions, different fracturing effects would still be obtained. The results of experiments could explain the different carbonate’s fracture modes, and effectively instruct the improvement of the on-site carbonate acid fracturing process.