  Light-cone gauge quantization procedures are given, for superstring theory on
$AdS_3$ space charged with NS-NS background, both in NSR and GS formalism. The
spacetime (super)conformal algebras are constructed in terms of the transversal
physical degrees of freedom. The spacetime conformal anomaly agrees with that
of covariant formalism, provided that the worldsheet conformal anomaly $c$
equals 26 or 15 for bosonic string or superstring, respectively. The spacetime
(super)conformal field theory is found to correspond to orbifold construction
on symmetric product space $\it{Sym_p} {\cal{M}}/Z_p$.
