The Dalitz decay η→γe+e− has been measured using the combined Crystal Ball and TAPS photon detector setup at the electron accelerator MAMI-C. Compared to the most recent transition form-factor measurement in the e+e− channel, statistics have been improved by one order of magnitude. The e+e− invariant mass distribution shows a deviation from the QED prediction for a point-like particle, which can be described by a form-factor. Using the usual monopole transition form-factor parameterization, F(m2)=(1−m2/Λ2)−1, a value of Λ−2=(1.92±0.35(stat)±0.13(syst)) GeV−2 has been determined. This value is in good agreement with a recent measurement of the η Dalitz decay in the μ+μ− channel and with recent form-factor calculations. An improved value of the branching ratio BR(η→γe+e−)=(6.6±0.4(stat)±0.4(syst))⋅10−3 has been determined.