In [1], the authors proved that there is a union D of a finite number of hypersurfaces in the complex projective space P n(C) such that for every entire curve f in P n(C) if the spherical derivative f# of f is bounded on f−1(D), then f# is bounded on the entire complex plane, and hence, f is a Brody curve. In this paper, we shall give the counterpart of their result on the normal family of holomorphic mappings.