A measurement of the cross-section for Z-boson production in the forward region of pp collisions at 8 TeV centre-of-mass energy is presented. The measurement is based on a sample of Z -> e(+)e(-) decays reconstructed using the LHCb detector, corresponding to an integrated luminosity of 2.0 fb(-1). The acceptance is defined by the requirements 2.0 < eta < 4.5 and p(T) > 20 GeV for the pseudorapidities and transverse momenta of the leptons. Their invariant mass is required to lie in the range 60-120 GeV. The cross-section is determined to be sigma(pp -> Z -> e(+)e(-)) = 93.81 +/- 0.41(stat) +/- 1.48(syst) +/- 1.14(lumi) pb, where the first uncertainty is statistical and the second reflects all systematic effects apart from that arising from the luminosity, which is given as the third uncertainty. Differential cross-sections are presented as functions of the Z-boson rapidity and of the angular variable phi*, which is related to the Z-boson transverse momentum.