Dark and baryonic matter contribute comparable energy density to the present Universe. The dark matter may also be responsible for the cosmic positron/electron excesses. We connect these phenomena with Dirac seesaw for neutrino masses. In our model (i) the dark matter relic density is a dark matter asymmetry generated simultaneously with the baryon asymmetry so that we can naturally understand the coincidence between the dark and baryonic matter; (ii) the dark matter mostly decays into the leptons so that its decay can interpret the anomalous cosmic rays with positron/electron excesses. PACS numbers: 98.80.Cq, 95.35.+d, 14.60.Pq, 11.30.Fs Precise cosmological observations indicate that dark and baryonic matter have different properties but contribute comparable energy density to the present Universe. This intriguing coincidence inspires us to propose a common origin for the creation and evolution of the dark and baryonic matter. Since the baryonic matter currently exists because of a matter-antimatter asymmetry, the dark matter relic density may also be an asymmetry between the dark matter and dark antimatter [1,2,3,4]. The dark matter asymmetry and the baryon asymmetry may originate from decays of the same heavy particles, so that their coincidence is not surprising at all. On the other hand, recently cosmic-ray data [5,6,7,8,9] suggest [10] that (i) the dark matter should dominantly annihilate or decay into leptons with a large cross section or a long life time; (ii) the dark matter annihilation or decay should be consistent with the constraints from the observations on the gamma and neutrino fluxes. In this paper we explain these phenomena in a unified scenario where the neutrino masses originate through the Dirac seesaw mechanism [11].We extend the standard model (SM) with a global U (1) lepton × U (1) dark symmetry and include additional particles: singlet right-handed neutrino ν R (1, 1, 0)(1, 1), heavy doublet scalar η(1, 2, −1/2)(0, −1), charged singlet scalar ξ(1, 1, 1)(−2, 0), and neutral singlet scalars σ(1, 1, 0)(0, −1) and χ(1, 1, 0)(−2, −1), where the transformations are given under the SM gauge group SU (3) c × SU (2) L × U (1) Y and the global symmetry U (1) lepton × U (1) dark . For simplicity, we only present the relevant part of the Lagrangian for purpose of demonstration,Here ψ L (1, 2, −1/2)(1, 0) and φ(1, 2, −1/2)(0, 0), respectively, are the SM lepton and Higgs doublets. The righthanded neutrinos neither have Yukawa couplings with the SM Higgs doublet nor have Majorana masses as a result of the U (1) lepton ×U (1) dark conservation. The global symmetry U (1) lepton will be exactly conserved at any energy scales while the global symmetry U (1) dark will be spontaneously broken above the weak scale. The singlet scalar σ acquires a vacuum expectation value (VEV) to break U (1) dark and then induces a small VEV of the heavy doublet scalars η after the electroweak symmetry breaking by φ ≃ 174 GeV,Therefore through the Dirac seesaw mechanism [11], the neutrinos obtain very small Dirac masses n...