The leaching of cobalt from cobalt-bearing ternary sulfide with sulfuric acid solution under atmospheric pressure was investigated. The influence of stirring speed, leaching temperature, H₂SO₄ concentration, and particle size on the leaching efficiency of cobalt was studied, and the kinetics analysis of cobalt leaching from the cobalt-bearing ternary sulfide was performed. The results showed that cobalt and iron were selectively leached with high efficiency (>99%) under the optimal conditions, while molybdenum and copper were enriched in residues. According to the analysis of the experimental data, the leaching of cobalt conformed to the shrinking core model with a solid product layer and was controlled by internal diffusion. The activation energy of the leaching reaction was 49.86 kJ/mol, and the reaction orders of H₂SO₄ concentration and particle size were 0.57 and -1.4, respectively.