Using 7.9fb(-1) of e(+)e(-) collision data collected at root s = 3.773 GeV with the BESIII detector at the BEPCII collider, we search for the massless dark photon with the flavor-changing neutral current processes D-0 -> omega gamma' and D-0 -> gamma gamma' for the first time. No significant signals are observed, and the upper limits at the 90% confidence level on the massless dark photon branching fraction are set to be 1.1 x 10(-5) and 2.0 x 10(-6) for D-0 -> omega gamma' and D-0 gamma gamma', respectively. These results provide the most stringent constraint on the new physics energy scale associated with cu gamma' coupling in the world, with the new physics energy scale related parameter |C|(2) + |C-5|(2) < 8.2 x 10(-17) GeV-2 at the 90% confidence level.