  Temporal and spatial variation of fine-structure constant $\alpha\equiv
e^2/\hbar c$ in cosmology has been reported in analysis of combination Keck and
VLT data. This paper studies this variation based on consideration of basic
spacetime symmetry in physics. Both laboratory $\alpha_0$ and distant
$\alpha_z$ are deduced from relativistic spectrum equations of atoms
(e.g.,hydrogen atom) defined in inertial reference system. When Einstein's
$\Lambda\neq 0$, the metric of local inertial reference systems in SM of
cosmology is Beltrami metric instead of Minkowski, and the basic spacetime
symmetry has to be de Sitter (dS) group. The corresponding special relativity
(SR) is dS-SR. A model based on dS-SR is suggested. Comparing the predictions
on $\alpha$-varying with the data, the parameters are determined. The best-fit
dipole mode in $\alpha$'s spatial varying is reproduced by this dS-SR model.
$\alpha$-varyings in whole sky is also studied. The results are generally in
agreement with the estimations of observations. The main conclusion is that the
phenomenon of $\alpha$-varying cosmologically with dipole mode dominating is
due to the de Sitter (or anti de Sitter) spacetime symmetry with a Minkowski
point in an extended special relativity called de Sitter invariant special
relativity (dS-SR) developed by
Dirac-In\"{o}n\"{u}-Wigner-G\"{u}rsey-Lee-Lu-Zou-Guo.
