On an n-dimensional complete manifold M, consider an h-almost gradient Ricci soliton, which is a generalization of gradient Ricci solitons and $(\lambda , n + m)$-Einstein manifolds. In this talk, we show that if the manifold is Bach-flat and $dh/du > 0$, then the manifold M is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. When the dimension of M is four, the metric is locally conformally flat.