The elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity (|y| < 0.7) is measured in Pb-Pb collisions at sNN=2.76 TeV with ALICE at the LHC. The particle azimuthal distribution with respect to the reaction plane can be parametrized with a Fourier expansion, where the second coefficient (v2) represents the elliptic flow. The v2 coefficient of inclusive electrons is measured in three centrality classes (0–10%, 10–20% and 20–40%) with the event plane and the scalar product methods in the transverse momentum (pT) intervals 0.5–13 GeV/c and 0.5–8 GeV/c, respectively. After subtracting the background, mainly from photon conversions and Dalitz decays of neutral mesons, a positive v2 of electrons from heavy-flavour hadron decays is observed in all centrality classes, with a maximum significance of 5.9σ in the interval 2 < pT < 2.5 GeV/c in semi-central collisions (20–40%). The value of v2 decreases towards more central collisions at low and intermediate pT (0.5 < pT < 3 GeV/c). The v2 of electrons from heavy-flavour hadron decays at mid-rapidity is found to be similar to the one of muons from heavy-flavour hadron decays at forward rapidity (2.5 < y < 4). The results are described within uncertainties by model calculations including substantial elastic interactions of heavy quarks with an expanding strongly-interacting medium.[Figure not available: see fulltext.]