  We study the superstring theory on pp-wave background with NSNS-flux that is
realized as the Penrose limit of AdS_3 x S^3 x M^4, where M^4 is T^4 or
T^4/Z_2(~ K3). Quantizing this system in the covariant gauge, we explicitly
construct the space-time supersymmetry algebra and the complete set of DDF
operators. We analyse the spectrum of physical states by using the spectrally
flowed representations of current algebra. This spectrum is classified by the
``short string sectors'' and the ``long string sectors'' as in AdS_3 string
theory. The states of the latter propagate freely along the transverse plane of
pp-wave background, but the states of the former do not. We compare the short
string spectrum with the BPS and almost BPS states which have large R-charges
in the symmetric orbifold conformal theory, which is known as the candidate of
dual theory of superstrings on AdS_3 x S^3 x M^4. We show that every short
string states can be embedded successfully in the single particle Hilbert space
of symmetric orbifold conformal theory.
