The behaviors of indium and silver in the acid leaching process of complex zinc sulfide concentrate were studied under high pressure. The effects of leaching temperature, leaching time, sulfuric acid concentration, oxygen partial pressure, particle size and ratio of solid to liquid on the indium leaching rate and the rate of silver entering leaching residue were examined, and the leaching kinetics in initial leaching stage was studied. The results show that the indium leaching rate can reach more than 76% and the rate of silver entering leaching residue is over 98% under the optimum conditions of leaching temperature 150℃, leaching time 90 min, sulfuric acid concentration 152 g/L, oxygen partial pressure 1.2 MPa, particle size <45 mm and ratio of solid to liquid 5 mL/g. Besides, the indium leaching in initial leaching stage is in line with shrinking core model, controlled by the surface chemical reaction, and the apparent activation energy is 70.67 kJ/mol.