  We completely accomplish the canonically covariant quantization of
Ramond-Neveu-Schwarz (RNS) superstrings in the pp-wave background with a
non-zero flux of the NS-NS antisymmetric two-form field. Here this flux is
equivalent to a nonvanishing torsion. In this quantization, general operator
solutions, which satisfy the entire equation of motion and all the canonical
(anti)commutation relations, play an important role. The whole of covariant
string coordinates and fermions can be composed of free modes. Moreover,
employing covariant free-mode representations, we calculate the anomaly in the
super-Virasoro algebra and determine the number of dimensions of spacetime and
the ordering constant from the nilpotency condition of the BRST charge in the
pp-wave background with the flux.
