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The kinetic behavior of leaching copper from low grade copper oxide ore was investigated. The effects of leaching temperature, H_2SO_4 concentration, particle size of crude ore and agitation rate on the leaching efficiency of copper were also evaluated. And the kinetic equations of the leaching process were obtained. The results show that the leaching process can be described with a reaction model of shrinking core. The reaction can be divided into three stages. The first stage is the dissolution of free copper oxide and copper oxide wrapped by hematite-limonite ore. At this stage, the leaching efficiency is very fast (leaching efficiency is larger than 60%). The second stage is the leaching of diffluent copper oxides, whose apparent activation energy is 43.26 kJ/mol. During this process, the chemical reaction is the control step, and the reaction order of H_2SO_4 is 0.433 84. The third stage is the leaching of copper oxide wrapped by hematite-limonite and silicate ore with apparent activation energy of 16.08 kJ/mol, which belongs to the mixed control.