To recover zinc at a low cost by roasting the dust in an oxidizing atmosphere and extracting zinc with a sulfuric acid aq. solution.

The dust is roasted at 700-950°C at first. As a result, iron and zinc in the dust are converted into a zinc ferrite insoluble in an acid and further other fine powder is also aggregated to be precipitated in the next extraction. Next, the extraction is performed with the sulfuric acid aq. solution to obtain a zinc sulfate aq. solution. In such a case, the quantity of sulfuric acid in the extraction sulfuric acid aq. solution is controlled preferably to 0.9-0.6 in the ratio expressed by (the quantity of the extraction sulfuric acid aq. solution)/(the equivalent quantity of sulfuric acid necessary for extracting total zinc in the dust). As a result, fine silicic acid present in the dust is converted into silica gel to prevent the filtration of the extraction residue from being disturbed. Since the clean zinc sulfate aq. solution containing no iron or silicon is obtained in this way, large equipment such as a wet zinc refining is unnecessary.