Ahanjideh, Akbari, Fakharan and Trevisan proposed a conjecture on the distribution of the Laplacian eigenvalues of graphs: for any connected graph of order n with diameter d ≥ 2 that is not a path, the number of Laplacian eigenvalues in the interval [n − d + 2, n] is at most n − d. We show that the conjecture is true and provide a family of graphs to show that the bound is best possible. This establishes an interesting relation between the spectral and classical parameters.