Fluid–rock interaction plays a critical function in physical and chemical processes associated with the formation and evolution of oil and gas reservoir space. In the diagenetic stage of shallow burial, the dissolution of carbonate rocks by acidic fluids is conducive to the development of secondary pore space in reservoirs. In contrast, the free drift experiment based on water bath instrument can simulate the dissolution process of carbonate rocks in shallow burial environment effectively. In order to study the shallow burial dissolution mechanism of carbonate rocks in different acid solutions, 14 samples of typical carbonate rocks of Sinian, Cambrian, Ordovician, Permian and Triassic ages in the Tarim and Sichuan Basins, China were used. The dissolution experiments on carbonate rocks in sulfuric acid, acetic acid, hydrochloric acid, silicic acid and carbonic acid at shallow burial temperature (30℃≤T≤90℃) were carried out using a water bath instrument. The PHREEQC software was used to simulate the dissolution of carbonate minerals, in order to compare the results of constant temperature water bath experiment. The results show that acid solutions have significant dissolution effect on shallow burial carbonate rocks when T = 50–60℃, which corresponds to the burial depth of 1500–2000 m in the Tarim Basin and 1110–1480 m in the Sichuan Basin. However, there were obvious differences in the dissolution and reformation of carbonate rocks in different acids. In particular, sulfuric acid solution produced by thermochemical sulfate reduction can significantly promote the dissolution of carbonate rocks, especially dolomitic limestone. Moreover, the dissolution of limestone reservoirs is stronger than that of dolomite reservoirs in shallow burial. The results will provide new insights into the study of dissolution laws and influencing factors of carbonate reservoir space and the evaluation and prediction of carbonate reservoir in China.