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