  In this paper the projective curvature invariants of a complex Finsler space
are obtained. By means of these invariants the notion of complex Douglas space
is then defined. A special approach is devoted to obtain the equivalence
conditions that a complex Finsler space should be Douglas. It is shown that any
weakly K\"{a}hler Douglas space is a complex Berwald space. A projective
curvature invariant of Weyl type characterizes the complex Berwald spaces. They
must be either purely Hermitian of constant holomorphic curvature or non purely
Hermitian of vanish holomorphic curvature. The locally projectively flat
complex Finsler metrics are also studied
