Let(M,g)be an n≥ 5 dimensional smooth compact Riemannian manifold of positive Yamabe type,which is not conformally equivalent to the standard sphere.We prove compactness of conformal metrics of g with positive constant Q-curvature provided that(M, g)is locally conformally at,or 5 ≤ n ≤ 9.We also prove the compactness result in dimension n ≥ 8,provided that the Weyl tensor of g does not vanish anywhere.This is a joint work with Jingang Xiong.