  It is known that a necessary condition for the existence of K\"ahler-Ricci
solitons is the vanishing of the modified Futaki invariant introduced by
Tian-Zhu. In a recent work of Berman-Nystr\"om, it was generalized for
(singular) Fano varieties and the notion of algebro-geometric stability of the
pair $(M,V)$ of a Fano manifold $M$ and a holomorphic vector field $V$ was
introduced. In this paper, we propose a method of computing the modified Futaki
invariant for Fano complete intersections in projective spaces.
