  We construct an asymptotically flat Morris-Thorne wormhole solution supported
by anisotropic matter fluid and a vector field which is coupled to gravity in a
non-minimal way with broken Abelian gauge symmetry. In this paper, a specific
shape function is considered. We find that the ansatz of vector field plays a
significant role in determining the spacetime geometry of the wormhole. If
there exists the electrostatic potential only, the redshift function could be
considered as a constant value, implying the vanishing tidal force. However,
when the vector potential in radial-direction is involved, the r-component of
extended Maxwell equations at the wormhole's throat is invalid. To solve this
issue, a thin shell is introduced near the throat, dividing the spacetime into
two parts. Furthermore, it is proved that the spacetime geometry of wormhole
could be smooth at junction position if the expressions of redshift function
and vector potential are given appropriately. Finally, the energy conditions
and the volume integral quantifer are explored.
