  In this paper, we investigate the supercategories consisting of supermodules
over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We
prove that these supercategories provide a supercategorification of a certain
family of quantum superalgebras and their integrable highest weight modules. We
show that, by taking a specialization, we obtain a supercategorification of
quantum Kac-Moody superalgebras and their integrable highest weight modules.
