Recent observations show that the electromagnetic fine-structure constant , \alpha _ { e } , may vary with space and time .
In the framework of Finsler spacetime , we propose here an anisotropic cosmological model , in which both the spatial and temporal variations of \alpha _ { e } are allowed .
Our model naturally leads to the dipole structure of \alpha _ { e } , and predicts that the dipole amplitude increases with time .
We fit our model to the most up-to-date measurements of \alpha _ { e } from the quasar absorption lines .
It is found that the dipole direction points towards ( l,b ) = ( 330.2 ^ { \circ } \pm 7.3 ^ { \circ } , -13.0 ^ { \circ } \pm 5.6 ^ { \circ } ) in the galactic coordinates , and the anisotropic parameter is b _ { 0 } = ( 0.47 \pm 0.09 ) \times 10 ^ { -5 } , which corresponds to a dipole amplitude ( 7.2 \pm 1.4 ) \times 10 ^ { -8 } at redshift z = 0.015 .
This is well consistent with the upper limit of the variation of \alpha _ { e } measured in the Milky Way .
We also fit our model to the Union2.1 type Ia supernovae , and find that the preferred direction of Union2.1 is well consistent with the dipole direction of \alpha _ { e } .