Extracting valuable elements from coal gangue is an important method for the utilization of coal gangue. In order to obtain the suitable technological conditions and the acid leaching kinetic model of leaching aluminum and iron ions from high-iron and low-aluminum coal gangue, the effects of calcination temperature, calcination time, and acid types on the leaching results of aluminum and iron ions are studied. The results show that when the gangue is calcined at 675 °C for 1 h, then the calcined gangue powder is leached by 6 mol/L hydrochloric acid at 93 °C for 4 h, the leaching ratio of iron ions is more than 90%, and that of aluminum ions is more than 60%. Furthermore, the acid leaching kinetic equations at 30 °C, 50 °C, 70 °C, and 90 °C are studied by three kinetic models, and the apparent activation energies of the reactions are calculated by the Arrhenius formula. The results show that the leaching behavior of aluminum and iron ions conformed to the “mixing control” model equation: “(1 − x)−1/3 − 1 + 1/3ln(1 − x) = kt + b”. The apparent activation energies of aluminum and iron ions are 55.5 kJ/mol and 55.8 kJ/mol, respectively. All these indicate that the acid leaching process is controlled by the “mixing control”.