In this paper, we prove the compactness theorem for gradient Ricci solitons. Let $(M_{ \alpha}, g_{ \alpha})$ be a sequence of compact gradient Ricci solitons of dimension $n\geq 4$, whose curvatures have uniformly bounded $L^{ \frac{ n}{ 2}}$ norms, whose Ricci curvatures are uniformly bounded from below with uniformly lower bounded volume and with uniformly upper bounded diameter, then there must exists a subsequence $(M_{ \alpha}, g_{ \alpha})$ converging to a compact orbifold $(M_{ \infty}, g_{ \infty})$ with finitly many isolated singularities, where $g_{ \infty}$ is a gradient Ricci soliton metric in an orbifold sense.
Categories: math.DG