It is known that for a weakly interacting Bose-Einstein condensate (BEC), t
he assumption of a two-body delta interaction described by a constant coupl
ing strength gives rise to a divergent ground-state energy. A similar diver
gence occurs in the spinor condensate in which the spin-spin interaction is
included in addition to the repulsive delta interaction. In this paper, we
examine, in the standard Bogoliubov approximation, the ground-state energy
of a homogeneous spinor BEC with hyperfine spin f = 1. The renormalized co
upling constants an calculated and expressed in terms of the bare ones usin
g the standard second-order perturbation method. With these renormalized co
upling constants, we show that the ultraviolet divergence of the ground-sta
te energy can be exactly eliminated. [S1050-2947(99)01106-3].