Recent observations show that the electromagnetic fine-structure constant,αe,may vary with space and time.In the framework of Finsler spacetime,we propose here an anisotropic cosmological model,in which both spatial and temporal variations of αe are allowed.Our model naturally leads to the dipole structure of αe,and predicts that the dipole amplitude increases with time.We fit our model to the most up-to-date measurements of αe from the quasar absorption lines.It is found that the dipole direction points towards (l,b)=(330.2° ± 7.3°,-13.0°± 5.6°) in galactic coordinates,and the anisotropic parameter is b0 =(0.47 ±0.09) × 10-5,which corresponds to a dipole amplitude (7.2 ± 1.4) × 10-8 at redshift z =0.015.This is consistent with the upper limit of the variation of αe measured in the Milky Way.We also fit our model to Union2.1 type Ia supernovae,and find that the preferred direction of Union2.1 is consistent with the dipole direction of αe.