The present invention relates to a plasma product or a serum product with an extremely low risk of viral contamination and a method for producing the same. Before treating plasma or serum to be used as a raw material for producing a plasma product or a serum product using a virus removal membrane, leucocytes contaminating the blood are removed. Thus, a plasma product or a serum product with an extremely low risk of viral contamination can be efficiently produced while preventing clogging. Since clogging scarcely arises, it is possible to carry out efficient filtration without applying an elevated pressure as the filtration proceeds.