  We discuss dual formulations of vortex strings (magnetic flux tubes) in the
four-dimensional ${\cal N} =1$ supersymmetric Abelian Higgs model with the
Fayet--Iliopoulos term in the superspace formalism. The Lagrangian of the model
is dualized into a Lagrangian of the $BF$-type described by a chiral spinor
gauge superfield including a 2-form gauge field. The dual Lagrangian is further
dualized into a Lagrangian given by a chiral spinor superfield including a
massive 2-form field. In both of the dual formulations, we obtain a superfield
into which the vortex strings and their superpartners are embedded. We show the
dual Lagrangians in terms of a superspace and a component formalism. In these
dual Lagrangians, we explicitly show that the vortex strings of the original
model are described by a string current electrically coupled with the 2-form
gauge field or the massive 2-form field.
