How to design a robust gene network to tolerate intrinsic kinetic parameter variations and to attenuate extrinsic environmental noises to a desired filtering level will be an important topic in metabolic engineering for biotechnological purpose or drug design for therapeutic purpose. At present, there is still no good systematic design method to achieve the robust gene network design. In this study, a gene network suffering from intrinsic kinetic parameter fluctuations and extrinsic environmental noises is modeled as Langevin equation with state-dependent stochastic noises. Based on the nonlinear stochastic filtering theory, a systematic gene circuit design method is proposed to achieve robust stability to tolerate intrinsic noises and to attenuate extrinsic noises to a prescribed filtering level. Computational simulations of a gene network are performed to illustrate the systematic design procedure and to confirm the performance of the proposed robust filtering circuit design in gene networks. The robust gene network design principles have not only yielded a comprehensive design theory of robust gene networks, but also gained valuable insights into the molecular noise filtering of gene networks. The proposed design method could precede the experimental biotechnological method to allow objective numerical improvement strategies for robust gene circuit designs.