The invention relates to a process for reducing the amount of sulphur compounds in a sulphur compounds contaminated wastewater stream, using a granular sludge treatment system (10) comprising anaerobic microorganisms, wherein the process comprises the steps of adding an aqueous nitrate solution to the wastewater stream, contacting the wastewater stream with the anaerobic microorganisms, and anoxic oxidation of at least part of the sulphur compounds in the sulphur compounds contaminated wastewater stream by the anaerobic microorganisms, resulting in a sulphur compounds depleted wastewater stream. The invention furthermore relates to such a granular sludge treatment system (10).