The invention discloses a process for bleaching waste paper pulp.The process includes steps of a, adding water into the waste paper pulp to dilute the waste paper pulp so as to obtain to-be-leached waste paper pulp solution with certain mass percentage concentration; b, adding a reducing agent sodium bisulfite to pre-treat the to-be-bleached waste paper pulp solution; c, sequentially adding chelating agents and sodium borohydride into pre-treated to-be-bleached waste paper pulp; d, adding acid-alkali buffer agents into the pre-treated to-be-bleached waste paper pulp and then carrying out supplementary bleaching on the pre-treated to-be-bleached waste paper pulp by the aid of a bleaching agent which is sodium hydrosulfite; e, washing paper pulp solution secondarily bleached at the step d to obtain required products.The process has the advantages that the operation process is simple and is low in cost and good in whiteness stability, and bleaching effects can be improved; the bleaching efficiency can be improved, the production cost can be reduced, and the quality of paper pulp can be improved; pollution can be reduced while an economic benefit is taken into consideration, and the process can be widely applied to recycling waste paper.