Fiber networks with out-of-plane auxetic behavior have been sporadically investigated. One of the major challenges is to design such materials with giant negative Poisson's ratio over large deformations. Here in, we report a systematic investigation to create three-dimensional (3D) fiber networks in the form of needlepunched nonwoven materials with out-of-plane auxetic behavior over large deformations via theoretical modeling and extensive set of experiments. The experimental matrix has encapsulated the key parameters of the needlepunching nonwoven process. Under uniaxial tensile loading, the anisotropy coupled with local fiber densification in networks has yielded large negative Poisson's ratio (up to -5.7) specifically in the preferential direction. The in-plane and out-of-plane Poisson's ratios of fiber networks have been predicted and, subsequently, compared with the experimental results. Fiber orientation was found to be a core parameter that modulated the in-plane Poisson's ratio of fiber networks. A parametric analysis has revealed the interplay between the anisotropy of the fiber network and the out-of-plane Poisson's ratio based upon constant volume consideration.