Recently 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 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 the possible anisotropy of the universe. The magnitudes of anisotropy are all between 2-5 %, but the systematic uncertainty cannot be excluded. The directions of the privileged axis seem to differ from each other. The statistical significance is not high enough to make a convincing conclusion. Nevertheless, the contours in the plane obtained from four groups of SNe Ia have an overlap, centering at . Monte Carlo simulation shows that the anisotropy is unlikely to be caused by the selection effect.