Abstract. Let L be a finite lattice with atleast two atoms and W (L) = {x | there exists y ∈ L such that x y }. The incomparability graph of L, denoted by Γ (L), is a graph with vertex set W (L) and two distinct vertices a, b ∈ W (L) are adjacent if and only if they are incomparable. In this paper, we study the incomparability graphs of lattices. We prove that, a disconnected graph is a graph of a lattice L if and only if L is of the form L1 L2. We prove that, Γ (L) cannot be an n-gon for any n ≥ 5. Some properties of incomparability graphs are obtained.