  We perform canonical quantization of the open Neveu-Schwarz-Ramond (NSR)
superstrings in the background of a D-brane with the NS B-field. If we choose
the mixed boundary condition as a primary constraint, it generates a set of
secondary constraints. These constraints are easily solved and as a result, the
noncommutative geometry in the bosonic string theory is extended to the
superspace. Solving the constraint conditions we also find that the Hamiltonian
for the superstring is equivalent to a free superstring Hamiltonian on the
target space with the effective open string metric G.
