  In this paper, we study an anisotropic universe model with Bianchi-I metric
using Joint Light-curve Analysis (JLA) sample of type Ia supernovae (SNe Ia).
Because light-curve parameters of SNe Ia vary with different cosmological
models and SNe Ia samples, we fit the SNe Ia light-curve parameters and
cosmological parameters simultaneously employing Markov Chain Monte Carlo
method. Therefore, the results on the amount of deviation from isotropy of the
dark energy equation of state ($\delta$), and the level of anisotropy of the
large-scale geometry ($\Sigma_0$) at present, are totally model-independent.
The constraints on the skewness and cosmic shear are $-0.101<\delta<0.071$ and
$-0.007<\Sigma_0<0.008$. This result is consistent with a standard isotropic
universe ($\delta=\Sigma_0=0$). However, a moderate level of anisotropy in the
geometry of the Universe and the equation of state of dark energy, is allowed.
Besides, there is no obvious evidence for a preferred direction of anisotropic
axis in this model.
