  In this paper, we consider the averaging principle for one dimensional
stochastic Burgers equation with slow and fast time-scales. Under some suitable
conditions, we show that the slow component strongly converges to the solution
of the corresponding averaged equation. Meanwhile, when there is no noise in
the slow component equation, we also prove that the slow component weakly
converges to the solution of the corresponding averaged equation with the order
of convergence $1-r$, for any $0<r<1$.
