Decays of b hadrons into final states containing a D-0 meson and a muon are used to measure the b (b) over bar; production cross-section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC. In the pseudorapidity interval 2 < eta < 6 and integrated over all transverse momenta we find that the average cross-section to produce b-flavoured or (b) over bar -flavoured hadrons is (75.3 +/- 5.4 +/- 13.0) mu b. (C) 2010 CERN. Published by Elsevier B.V. All rights reserved.