A monomer with reactive double bonds was mixed with a liquid crystal and polymerized under UV irradiation in various phases of the liquid crystal. The polymer networks formed are found to be anisotropic and fiber-like, if the monomer is polymerized in an oriented liquid crystal state. The orientational order of the polymer network is shown to depend on that of the liquid crystal. After polymerization, the polymer network, in turn, is found to affect the orientation of the liquid crystal significantly. It induces birefringence in nematics at temperatures just above the nematic-isotropic phase transition.