  We present in this paper a covariant quantization of the ``massive'' vector
field on de Sitter (dS) space based on analyticity in the complexified
pseudo-Riemanian manifold. The correspondence between unitary irreducible
representations of the de Sitter group and the field theory on de Sitter
space-time is essential in our approach. We introduce the Wightman-G\"arding
axiomatic for vector field on dS space. The Hilbert space structure and the
unsmeared field operators $K_\alpha(x)$ are also defined. This work is in the
direct continuation of previous one concerning the scalar and the spinor cases.
