  Recent released Planck data and other astronomical observations show that the
universe may be anisotropic on large scales. This hints a cosmological
privileged axis in our anisotropic expanding universe. This paper proceeds a
modified redshift in anisotropic cosmological model as $
1+\tilde{z}(t,\hat{\textbf{p}})=\frac{a(t_{0)}}{a(t)}(1-A(\hat{\textbf{n}}.\hat{\textbf{p}}))$
(where $A$ is the magnitude of anisotropy ,$\hat{\textbf{n}}$ is the direction
of privileged axis, and $\hat{\textbf{p}}$ is the direction of each SNe Ia
sample to galactic coordinates) along with anisotropic parameter
$\delta=\frac{A(\hat{\textbf{n}}.\hat{\textbf{p}})}{1+A(\hat{\textbf{n}}.\hat{\textbf{p}})}$.
The luminosity distance is expanded with model-independent cosmographic
parameters as a function of modified redshift $\tilde{z}$. As the
transformation matrix $M(n\times n)$ is obtained to convert the Taylor series
coefficients of isotropic luminosity distance to corresponding anisotropic
parameters. These results culminate the magnitude of anisotropy about $\mid
A\mid \simeq 10^{-3}$ and the direction of preferred axis as
$(l,b)=(297^{-34}_{+34},3^{-28}_{+28})$, which are consistent with other
studies in $1-\sigma$ confidence level.
