A graph whose graphic metric space is isomorphic to some subspace of an l₁-space is called l₁-embeddable. A mono -4 -gons cyclohexane molecular graph refers to a 2 -connected planar graph embedded in a plane with exactly one quadrilateral face, the rest are hexagonal faces, and the inner vertices degree are 3 and the boundary vertices degree are 2 or 3. It is proved that when there are only two adjacent 3-degree vertices on the quadrilateral, the mono-4-gons cyclohexane graph is l₁-embeddable, and the others are not.