  We construct a crystal base of $U_q(\mathfrak{gl}(m|n))^-$, the negative half
of the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$. We give a combinatorial
description of the associated crystal $\mathscr{B}_{m|n}(\infty)$, which is
equal to the limit of the crystals of the ($q$-deformed) Kac modules
$K(\lambda)$. We also construct a crystal base of a parabolic Verma module
$X(\lambda)$ associated with the subalgebra $U_q(\mathfrak{gl}_{0|n})$, and
show that it is compatible with the crystal base of $U_q(\mathfrak{gl}(m|n))^-$
and the Kac module $K(\lambda)$ under the canonical embedding and projection of
$X(\lambda)$ to $U_q(\mathfrak{gl}(m|n))^-$ and $K(\lambda)$, respectively.
