Using an electron-positron collision data sample of 2.93 fb−1 collected at a center-of-mass energy of ffiffi s p ¼ 3.773 GeV with the BESIII detector, we present the first search for the radiative leptonic decay Dþ → γeþνe. The analysis is performed with a double-tag method. We do not observe a significant Dþ → γeþνe signal, and obtain an upper limit on the branching fraction of Dþ → γeþνe decay with the energy of radiative photon larger than 10 MeV of 3.0 × 10−5 at the 90% confidence level.