Forward top quark pair production is studied in pp collisions in the eb final state using a data sample corresponding to an integrated luminosity of 1.93 fb1 collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The cross-section is measured in a fiducial region where both leptons have a transverse momentum greater than 20 GeV and a pseudorapidity between 2.0 and 4.5. The quadrature sum of the azimuthal separation and the difference in pseudorapidities, denoted R, between the two leptons must be larger than 0.1. The b-jet axis is required to be separated from both leptons by a R of 0.5, and to have a transverse momentum in excess of 20 GeV and a pseudorapidity between 2.2 and 4.2. The cross-section is measured to bett¯=126±19stat±16syst±5lumifb$$ {\sigma}_{t\overline{t}}=126\pm 19\left(\mathrm{stat}\right)\pm 16\left(\mathrm{syst}\right)\pm 5\left(\mathrm{lumi}\right)\mathrm{f}\mathrm{b} $$where the first uncertainty is statistical, the second is systematic, and the third is due to the luminosity determination. The measurement is compatible with the Standard Model prediction.