Based on physicochemical properties of the scraps of spent aerospace magnetic materials, a roasting – magnetic separation followed by sulfuric acid leaching process was proposed to extract cobalt. Roasting was performed at 500 °C to remove organic impurity. Non-magnetic impurities were reduced by magnetic separation and then the raw material was sieved into desired particle sizes. Acid leaching was carried out to extract cobalt from the scraps and experimental parameters included agitation speed, particle size, initial concentration of sulfuric acid and temperature. Agitation speed higher than 300 r/min had a relatively small impact on the cobalt extraction. As the particle size reduced, the content of cobalt in the raw material decreases and the extraction of cobalt by acid leaching increased at first and decreased afterwards. Raising the initial concentration of sulfuric acid and temperature contributed to improve the cobalt extraction and the influence of temperature was more remarkable. SEM image revealed that the spent aerospace magnetic materials mainly existed in the sliced strip flake with a loose surface and porous structure. Under the experimental condition, the leaching rate of cobalt from the scraps in sulfuric acid solution could be expressed as ln(−ln(1 − α)) = lnk + nlnt. The apparent activation energy was found to be 38.33 kJ/mol and it was mainly controlled by the surface chemical reaction.