There is disclosed a novel method of recovering valuable metals from an industrial by-product containing copper and arsenic and at least one metal selected from among lead, zinc, iron, silver and cadmium, said method comprising leaching the by-product with sulfuric acid in an SO.sub.2 gas atmosphere at a temperature of 70.degree. C. or higher in the presence of a solid sulfide to thereby precipitate copper selectively as copper sulfide while dissolving other metal or metals in the leach solution and then separating the copper containing precipitate from the leach solution, said leach solution containing substantially no copper.