Summary: The weighted Myers’ theorem gives an upper bound estimate for the diameter of a complete Riemannian manifold with the \(\tau\)-Bakry-Émery curvature bounded from below by a positive number. The lower bound estimate for the diameter of a compact manifold is also an interesting question. In this paper, a gradient estimate for the potential function of a special \(\tau\)-quasi-almost-Einstein metric is established using the Hopf’s maximum principle. Based on it, a lower bound estimate for the diameter of this metric is derived.