The　energy　of　a　graph　is　defined　as　the　sum　of　the　absolute　values　of　all　eigenvalues　of　the　graph.　F.　Zhang,　H.　Li　[On　acyclic　conjugated　molecules　with　minimal　energies,　Discrete　Appl.　Math.　92　(1999)　71-84]　characterized　the　trees　with　a　perfect　matching　having　the　minimal　and　the　second　minimal　energies,　which　solved　a　conjecture　proposed　by　I.　Gutman　[Acyclic　conjugated　molecules,　trees　and　their　energies,　J.　Math.　Chem.　1　(1987)　123-143].　In　this　letter,　for　a　given　positive　integer　d　we　characterize　the　tree　with　the　minimal　energy　having　diameter　at　least　d.　As　a　corollary,　we　also　characterize　the　tree　with　the　minimal　Hosoya　index　having　diameter　at　least　d.　(c)　2005　Elsevier　Ltd.　All　rights　reserved.