Brewer’s spent grain (BSG) was evaluated for bleached pulp production. Two cellulose pulps with different chemical compositions were produced by soda pulping: one from the original raw material and the other from material pretreated by dilute acid. Both of them were bleached by a totally chlorine-free sequence performed in three stages, using 5% hydrogen peroxide in the two initial, and a 0.25 N NaOH solution in the last one. Chemical composition, kappa number, viscosity, brightness and yield of bleached and unbleached pulps were evaluated. The high hemicellulose (28.4% w/w) and extractives (5.8% w/w) contents in original BSG affected the pulping and bleaching processes. However, soda pulping of acid pretreated BSG gave a cellulose-rich pulp (90.4% w/w) with low hemicellulose and extractives contents (7.9% w/w and <3.4% w/w, respectively), which was easily bleached achieving a kappa number of 11.21, viscosity of 3.12 cp, brightness of 71.3%, cellulose content of 95.7% w/w, and residual lignin of 3.4% w/w. Alkaline and oxidative delignification of acid pretreated BSG was found as an attractive approach for producing high-purity, chlorine-free cellulose pulp.