  Recent released Planck data and other astronomical observations show that the
universe may be anisotropic on large scales. Inspired by this, anisotropic
cosmological models have been proposed. We note that the Finsler-Randers
spacetime provides an appropriate framework for the anisotropic cosmology. By
adding an arbitrary 1-form to the Friedmann-Robertson-Walker (FRW) line
element, a privileged axis in the universe is picked out. The distance-redshift
relation is modified to be direction-dependent. We wish that the anisotropic
cosmological model may be tested crossly by independent observations. Type-Ia
supernovae (SNe Ia) calibrated from four different light curve fitters are used
to constrain possible anisotropy of the universe. The magnitudes of anisotropy
are all between 2% --- 5%, but the systematic uncertainty cannot be excluded.
The directions of privileged axis seem to differ from each other. The
statistical significance is not high enough to make a convincing conclusion.
Nevertheless, the $1\sigma$ contours in the $(l,b)$ plane obtained from four
groups of SNe Ia have an overlap, centering at $(l,b)\approx
(170^{\circ},0^{\circ})$. Monte Carlo simulation shows that the anisotropy is
unlikely to be caused by selection effect.
