To provide a new method by which only cobalt compds. included in a waste lithium cell or the like can be selectively dissolved at high efficiency while the dissolution of admixed other metals is suppressed as much as possible.

After a cobalt compd. is immersed in sulfuric acid diluted with water, a reducing agent is added. Or, the cobalt compd. is immersed in an aq. soln. in which a reducing agent is previously dissolved in a diluted mineral acid. The compd. is dissolved under the condition of 0.01 mol/l to 0.5 mol/l concn. of the sulfuric acid aq. soln. and 0.05 to 2 mol add amt. of the reducing agent to 1 mol of the cobalt compd is preferable. By dissolving the cobalt compd. with the diluted sulfuric acid and the reducing agent, the dissolving operation is simplified and the method is excellent in safeness and improved from the economical viewpoint.