  We make use of the method of modulus of continuity \cite{K-N-S} and Fourier
localization technique \cite{A-H} to prove the global well-posedness of the
critical Burgers equation $\partial_{t}u+u\partial_{x}u+\Lambda u=0$ in
critical Besov spaces $\dot{B}^{\frac{1}{p}}_{p,1}(\mathbb{R})$ with
$p\in[1,\infty)$, where $\Lambda=\sqrt{-\triangle}$.
