We propose a Finsler spacetime scenario of the anisotropic universe. The Finslerian universe requires both the fine-structure constant and the accelerating cosmic expansion to have a dipole structure and the directions of these two dipoles to be the same. Our numerical results show that the dipole direction of the SnIa Hubble diagram locates at (l, b) = (314.6 degrees +/- 20.3 degrees,-11.5 degrees +/- 12.1 degrees) with magnitude B = (-3.60 +/- 1.66) x 10(-2). The dipole direction of the fine-structure constant locates at (l, b) = (333.2 degrees +/- 8.8 degrees,-12.7 degrees +/- 6.3 degrees) with magnitude B = (0.97 +/- 0.21) x10(-5). The angular separation between the two dipole directions is about 18.2 degrees.