Given an arbitrary graph G = (V, E) and an interval graph H = (V, F) with E ⊆ F we say that H is an interval completion of G. The graph H is called a minimal interval completion of G if, for any sandwich graph H′ = (V, F′) with E ⊆ F′ ⊂ F, H′ is not an interval graph. In this paper we give a O (n m) time algorithm computing a minimal interval completion of an arbitrary graph. The output is an interval model of the completion.