  In this paper, we present a theory of quantum electrodynamics with nonlocal
interaction, a main characteristic of the theory is that a charged particle
situated x^{mu} interacts with electromagnetic field situated y^{mu}, where
x^{mu}=y^{mu}+aA^{mu}, A^{mu} reads electromagnetic 4-potential, a is a
constant. All the action, the equations of motion of charged particle and
electromagnetic field are given. For the case of free fields, charged particle
and electromagnetic field obey the Dirac equation and the Maxwell equation of
free fields, respectively; for the case with interaction, both the equations of
motion of charged particle and electromagnetic field lead to current
conservation j^{mu}_{,mu}=0 naturally. The theory is Lorentz invariant and
gauge invariant under a generalized gauge transformation, the generalized gauge
transformation can guarantee that the temporal gauge condition A^{0} holds or
the Lorentz gauge condition A^{mu}_{,mu}=0 holds, respectively. The theory
returns to the current QED when a=0. Finally, taking advantage of the
Lehmann-Symanzik-Zimmermann approach, we establish the corresponding quantum
theory.
