  We investigate (super) string theory on $AdS_3$ background based on an
approach of free field realization. We demonstrate that this string theory can
be reformulated as a string theory defined on a linear dilaton background along
the transverse direction (``Liouville mode'') and compactified onto $S^1$ along
a {\em light-like} direction.
  Under this reformulation we analyze the physical spectrum as that of a free
field system, and discuss the consequences when we turn on the Liouville
potential. The discrete light-cone momentum in our framework is naturally
interpreted as the ``winding number'' of the long string configuration and is
identified with the spectral flow parameter that is introduced in the recent
work by Maldacena and Ooguri \cite{MO}.
  Moreover we show that there exist infinite number of the on-shell chiral
primary states possessing the different light-cone momenta and the spectral
flow consistently acts on the space of chiral primaries. We observe that they
are also chiral primaries in the sense of space-time (or the conformal theory
of long string) and the spectrum of space-time $U(1)_R$ charge is consistent
with the expectation from the $AdS_3/CFT_2$-duality. We also clarify the
correspondence between our framework and the symmetric orbifold theory of
multiple long string system \cite{HS2}.
