  Taking the quantum electrodynamics (QED) effect into account, we investigate
the geometrical-optics appearance of the Euler-Heisenberg (EH) black hole (BH)
under the different accretion flows context, which depends on the BH space-time
structure and different sources of light. The more significant magnetic charge
leads to the smaller shadow radius for the EH BH, while the different values of
the EH parameter do not ruin it. Different features of the corresponding
two-dimensional shadow images are derived for the three optically thin
accretion flow models. It is shown that the total observed intensity in the
static spherical accretion flow scenario leads than that of the infalling
spherical accretion flow under same parameters, but the size and position of
the EH BH shadows do not change in both of these accretions flows, implying
that the BH shadow size depends on the geometric space-time and the shadows
luminosities rely on the accretion flow morphology. Of particular interest is
that a thin disk accretion model illuminated the BH, we found that the
contribution of the lensing ring to the total observed flux is less than 5\%,
and the photon ring is less than 2\%, indicating that the direct emission
dominates the optical appearance of the EH BH. It is also believed that the
optical appearance of the BH image depends on the accretion disk radiation
position in this scenario, which can serve as a probe for the disk structure
around the active galactic nucleus (AGN) of M87^{*} like.
