  Lorentz-invariant non-commutative QED (NCQED) is constructed such that it
should be a part of Lorentz-invariant non-commutative standard model (NCSM), a
subject to be treated in later publications. Our NCSM is based on Connes'
observation that the total fermion field in the standard model may be regarded
as a bi-module over a flavor-color algebra. In this paper, it is shown that
there exist two massless gauge fields in NCQED which are interchanged by $C'$
transformation. Since $C'$ is reduced to the conventional charge conjugation
$C$ in the commutative limit, the two gauge fields become identical to the
photon field in the same limit, which couples to only four spinors with charges
$\pm 2,\pm 1.$ Following Carlson-Carone-Zobin, our NCQED respects Lorentz
invariance employing Doplicher-Fredenhagen-Roberts' algebra instead of the
usual algebra with constant $\theta^{\mu\nu}$. In the new version
$\theta^{\mu\nu}$ becomes an integration variable. We show using a simple NC
scalar model that the $\theta$ integration gives an {\it invariant} damping
factor instead of the oscillating one to the nonplanar self-energy diagram in
the one-loop approximation. Seiberg-Witten map shows that the $\theta$
expansion of NCQED generates exotic but well-motivated derivative interactions
beyond QED with allowed charges being only $0, \pm 1, \pm 2$.
