In this talk, we will consider the local null controllability of Burgers equation in $\mathbb{R}$. The control is assumed to be distributed along an equidistributed set $\omega$. We first prove a uniform upper bound on costs of local null controls for Burgers equation on a sequence $\{\Omega_n\}_{n\geq 1}$ of increasing domains, where the controls are acted on $\Omega_n\bigcap \omega$. Then, letting $n$ tend to infinity, we obtain the main result (This is a joint work with Dr. Can Zhang).