In this paper, we classify n-dimensional ($n\ge 4$) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite quotient of the Gaussian shrinking soliton R^4 or the round cylinder S^3 x R. More generally, for $n\ge 5$, a Bach-flat
gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Gaussian shrinking soliton $R^n$ or the
product $N^{n-1}xR$, where $N^{n-1}$ is Einstein.