  In this paper, we revisit the model of bosonic matter in the form of a free
complex scalar field with a nontrivial wormhole spacetime topology supported by
a free phantom field. We obtain a new type of boson star with wormhole
solutions, in which the complex scalar field possess full parity-odd symmetry
with respect to the two asymptotically flat spacetime regions. When the size of
the throat is small, The behavior of boson stars with wormhole approaches that
of boson stars. When the size of the throat is intermediate, the typical
spiraling dependence of the mass and the particle number on the frequency of
the boson stars is replaced by a loop structure. However, as the size becomes
relatively large, the loop structure will also disappear. In particular, The
complex scalar field could form two boson stars with opposite phase differences
with respect to the two spacetime regions in the limit of vanishing throat
size. We analyze the properties of this new type of boson stars with wormhole
and further show that the wormhole spacetime geometry.
