Hydrolyzes p-nitrophenyl beta-D-glucoside, p-nitrophenyl beta-D-galactoside, p-nitrophenyl beta-D-xyloside, p-nitrophenyl beta-D-fucoside, p-nitrophenyl beta-L-arabinoside, cello-oligosaccharides and laminaribiose. Hydrolysis of terminal, non-reducing beta-D-glucosyl residues with release of beta-D-glucose. Belongs to the glycosyl hydrolase 1 family.