It is intended to provide a process for producing bleached pulp in which unbleached pulp obtained by cooking a lignocellulose material is subjected t o alkali/oxygen bleaching, treated with peroxomonosulfuric acid, and further a multi-stage chlorine-free bleaching treatment starting from a chlorine di oxide bleaching treatment is carried out; a process for producing bleached p ulp in which the unbleached pulp is subjected to alkali/oxygen bleaching, an d then subjected to a chlorine-free bleaching treatment or a totally chlorin e-free bleaching treatment to bleach the pulp so as to have a whiteness of 7 0 to 89%, then the pulp is treated with peroxomonosulfuric acid; and paper p roduced at a papermaking pH of 6 or below using the bleached pulp obtained b y such a production process. A process for efficiently producing bleached pu lp in which the brown color is improved in the chlorine-free bleaching and t he bleaching cost is reduced and paper produced in an acidic papermaking con dition using the bleached pulp are provided.