A measurement of the top-pair production cross-section at a centre-of-mass energy of 7 TeV using proton-proton collisions with 36 pb-1 of data collected by CMS at the Large Hadron Collider is presented. The analysis is performed using the nal state that consists of one isolated electron with jets, one of which is required to be identified as being consistent with including the decay of a B hadron. The measured cross-section with three or more selected jets is 169 +/- 13(stat:)+37 +32(sys:)+8 -7(lumi:) pb and 197 +/- 17(stat:)+38 -35(sys:)+9 -8(lumi:) pb for four or more jets. The results are consistent with NLO and approximate NNLO theoretical predictions.