Recently, the Dark Matter Particle Explorer (DAMPE) experiment released the new measurement of the total cosmic e(+) e(-) flux between 25 GeV and 4.6 TeV, which indicates a spectral softening at around 0.9 TeV and a tentative peak at around 1.4 TeV. We utilize a scalar dark matter (DM) model to explain the DAMPE peak by XX -> Z'Z' -> l (l) over barl'(l) over bar 'l with an additional anomaly-free gauged U (l) family symmetry, in which X, Z'and l((')) denote, respectively, the scalar DM, the new gauge boson, and l((')) = e, mu, tau, with m(x) similar to m(z)' similar to 2 x 1.5 (TeV). We first illustrate that the minimal framework Gsm X U(l)(Y') with the above mass choices can explain the DAMPE excess, which, however, be excluded by LHC constraints from the Z' searches. Then, we study a nonminimal framework G(SM) X U(l)(Y') x U(i)(Y") in which U(l)(Y") mixes with U(l)(Y'). We show that such a framework can interpret the DAMPE data and at the same time survive all other constraints including the DM relic abundance, DM direct detection, and collider bounds. We also investigate the predicted e(+) e(-) spectrum in this framework and find that the mass splitting Delta m = m(x) - m(z") should be less than about 17 GeV to produce the peaklike structure.