  Geometric quantization transforms a symplectic manifold with Lie group action
to a unitary representation. In this article, we extend geometric quantization
to the super setting. We consider real forms of contragredient Lie supergroups
with compact Cartan subgroups, and study their actions on some pseudo-K\"ahler
supermanifolds. We construct their unitary representations in terms of sections
of some line bundles. These unitary representations contain highest weight
Harish-Chandra supermodules, whose occurrences depend on the image of the
moment map. As a result, we construct a Gelfand model of highest weight
Harish-Chandra supermodules. We also perform symplectic reduction, and show
that quantization commutes with reduction.
