In this paper, we study the covering dimension \(dim_{\mathcal {L}}\) of finite distributive lattices. By the Birkhoff’s representation theorem for finite distributive lattices, we prove that for any finite distributive lattice L, \(dim_{\mathcal {L}}(L) = ord_{\mathcal {L}}(\textrm{Max}(\mathcal {J}(L)))\) , where \(\textrm{Max}(\mathcal {J}(L))\) is the set of all maximal elements of join-irreducible elements of L. Based on the relationships between the covering dimension of topological spaces and that of bounded distributive lattices, we characterize the covering dimension of finite \(T_{0}\) spaces. Finally, we study the covering dimension of the linear sum, Cartesian product, lexicographic product and rectangular product of two finite distributive lattices.
