We construct a crystal base of Uq(gl(m|n))−, the negative half of the quantum superalgebra Uq(gl(m|n)). We give a combinatorial description of the associated crystal Bm|n(∞), which is equal to the limit of the crystals of the (q-deformed) Kac modules K(λ). We also construct a crystal base of a parabolic Verma module X(λ) associated with the subalgebra Uq(gl(0|n)), and show that it is compatible with the crystal base of Uq(gl(m|n))− and the Kac module K(λ) under the canonical embedding and projection of X(λ) to Uq(gl(m|n))− and K(λ), respectively.