For a smooth projective morphism between complex manifolds
with section, it is known that there exists a relative Albanese map.
If this map is principally polarized, the structure is well-known.
On the contrary, the structure of a general polarized relative
Albanese map is not known. In this talk, we will give a coordinate
of the local constant system and description of the monodromy
matrix. As an application, we give an explicite descriptionof
a relative compactification of an abelian fibration over a
punctured disk.