  In this paper, we solve a problem of Kobayashi posed in \cite{Ko4} by
introducing a Donaldson type functional on the space $F^+(E)$ of strongly
pseudo-convex complex Finsler metrics on $E$ -- a holomorphic vector bundle
over a closed K\"ahler manifold $M$. This Donaldson type functional is a
generalization in the complex Finsler geometry setting of the original
Donaldson functional and has Finsler-Einstein metrics on $E$ as its only
critical points, at which this functional attains the absolute minimum.
