Based on Cohen & Glashow's very special relativity (Cohen and Glashow in Phys. Rev. Lett. 97: 021601, 2006), we propose an anisotropic modification to the Friedmann-Robertson-Walker (FRW) line element. An arbitrarily oriented 1-form is introduced and the FRW spacetime becomes of the Randers-Finsler type. The 1-form picks out a privileged axis in the universe. Thus, the cosmological red-shift as well as the Hubble diagram of the type Ia supernovae (SNe Ia) becomes anisotropic. By directly analyzing the Union2 compilation, we obtain the privileged axis pointing to (l, b) = (304 degrees +/- 43 degrees,-27 degrees +/- 13 degrees) (68 % C.L.). This privileged axis is close to those obtained by comparing the best-fit Hubble diagrams in pairs of hemispheres. It should be noticed that the result is consistent with isotropy at the 1 sigma level since the anisotropic magnitude is D = 0.03 +/- 0.03.