Kaolinite-rich coal gangue contains a large amount of SiO₂ and Al₂O₃. In this work, the coal gangue was selected to leach the Al₂O₃ by using hydrochloric acid and then to leach the SiO₂ from the acid leaching slag by NaOH alkaline. The effects of acid leaching concentration, acid leaching temperature, acid leaching time and liquid-solid ratio on the leaching rate of Al₂O₃ from calcined coal gangue were investigated, and the effects of alkaline leaching conditions on the leaching rate of SiO₂ from acid leaching slag were also explored. The results show that when the conditions of acid leaching and alkali leaching are optimized by single variable experiment, the leaching rate of Al₂O₃ in coal gangue is 92.6%, and the leaching rate of SiO₂ in acid leaching residue is 99.1%. The study of the kinetic models of acid leaching and alkaline leaching processes shows that, the kinetics model of the acid leaching process of coal gangue is in accordance with the mixed control model of internal diffusion and chemical reaction, while the alkaline leaching agreed well with the chemical reaction control model. There is a good linear relationship between the logarithm of the apparent reaction rate constants ln k_c and ln k_b versus T^-1, for the acid leaching mixed control model and the alkaline leaching chemical reaction control model, respectively. In this paper, the kinetic rate equations of acid leaching process and alkali leaching process are also obtained. The results of this study can be used to guide the production of aluminum and silicon leaching from industrial coal gangue.