We study a nonthermal scenario in a two-Higgs doublet extension of the standard model (SM), augmented by a U(1)B-L gauge symmetry. In this setup, it is shown that the decay product of a weakly coupled scalar field just above the electroweak scale can generate visible and dark matter (DM) simultaneously. DM is unstable because of the broken B-L symmetry. The lifetime of DM (≈5×1025 sec) is found to be much longer than the age of the Universe, and its decay to the SM leptons at the present epoch can explain the positron excess observed at the AMS-02. The relic abundance and the direct detection constraint from Xenon-100 can rule out a large parameter space, just leaving the B-L breaking scale around ≈2-4 TeV. © 2013 American Physical Society.