A method that, regarding a process of refining molten iron, can increase the thermal margin and the amount of cold iron source to be used. A burner having jetting holes for jetting a fuel and a combustion supporting gas is provided at a leading end part of one lance that top-blows an oxidizing gas to molten iron contained in a converter-type vessel, or at a leading end part of another separate lance. A powdery auxiliary raw material or an auxiliary raw material processed into a powder form that is blown into the molten iron from the one lance or the other lance passes through a flame formed by the burner. This top-blowing lance for a converter is configured to secure a predetermined heating time and powder-fuel ratio. Also, a method for adding an auxiliary raw material and a method for refining of molten iron that use this top-blowing lance.