  In this paper, we get an inequality in terms of holomorphic sectional
curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma
from a complete Riemannian manifold to a complex Finsler manifold. We also show
that a strongly pseudoconvex complex Finsler manifold with semi-positive but
not identically zero holomorphic sectional curvature has negative Kodaira
dimension under an extra condition.
