Abstract: In this paper, we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kähler Finsler. As an application, we find any complete strongly convex and locally conformal pseudo-Kähler Finsler manifold, which is simply connected or whose fundamental group contains elements of finite order only, can be given a Kähler metric.

Key words:  Strongly pseudoconvex complex Finsler metric, Locally conformal pesudo-K?hler Finsler metric, K?hler metric