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We present a consistent \delta N formalism for curvature perturbations inanisotropic cosmological backgrounds. We employ our \delta N formalism tocalculate the power spectrum, the bispectrum and the trispectrum in models ofanisotropic inflation with the background gauge fields in Bianchi I universe.Our results coincide exactly with the recent results obtained from in-informalism. To satisfy the observational constraints the anisotropies generatedon power spectrum are kept small but large orientation-dependentnon-Gaussianities can be generated. We study the Suyama-Yamaguchi inequalityfor the amplitudes of the bispectrum and the trispectrum in the presence ofanisotropic shapes.

\delta N Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum