Considering the Cauchy problem for the Korteweg-de Vries-Burgers equationut + ux x x + ? lunate ?x 2 ? u + (u2)x = 0, u (0) = ? symbol , where 0 <? lunate , ? ? 1 and u is a real-valued function, we show that it is globally well-posed in Hs (s > s?), and uniformly globally well-posed in Hs (s > - 3 / 4) for all ? lunate ? (0, 1]. Moreover, we prove that for any T > 0, its solution converges in C ([0, T] ; Hs) to that of the KdV equation if ? lunate tends to 0.