Search for the time variation of the fundamental constants is motivated by various unification theories. Here we present constraints on the variation of the fine-structure constant $\alpha$($\equiv {e^2/\hbar c}$) obtained using UVES/VLT samples of QSO absorption systems. We find ${<\Delta\alpha/\alpha}>_{w}={(-0.06\pm0.06)\times10^{-5}}$ using 23 Mg II systems and the many-multiplet (MM) method. Well selected 15 Si IV systems provide ${<\Delta\alpha/\alpha}>_{w}={(0.15\pm0.43)\times10^{-5}}$. Absence of detectable variation in $\alpha$ is also confirmed by our new very high resolution ($R\sim 100,000$) observation of $z_{\rm abs}=1.1508$ toward HE 0515–4414 using HARPS on the ESO 3.6m telescope.