The notion of holomorphic bisectional curvature for a complex Finsler space $(M,F)$ is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holo-morphic bisectional curvature. For the class of generalized Einstein complex Finsler spaces some results concerning the holomorphic bisectional curvature are also given.