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.