  We propose a weak Galerkin(WG) finite element method for solving the
one-dimensional Burgers' equation. Based on a new weak variational form, both
semi-discrete and fully-discrete WG finite element schemes are established and
analyzed. We prove the existence of the discrete solution and derive the
optimal order error estimates in the discrete $H^1$-norm and $L^2$-norm,
respectively. Numerical experiments are presented to illustrate our theoretical
analysis.
