The phrase "a grim eye" is correct and usable in written English.
It can be used to describe someone observing a situation with a serious or stern demeanor, often implying disapproval or concern.
Example: "She watched the proceedings with a grim eye, knowing the implications of their decisions."
Alternatives: "a stern gaze" or "a serious look".
The government agreed reluctantly to the mission and keeps a grim eye on it.
Love… is immersed in fathoms of disco and synth-pop past, but with a grim eye on a parlous present of bankers' bonuses and tough times, in which our jilted, exiled lover rediscovers the radical pleasure of "drinking tea like Tony Benn".
Pessimistic companies tend to slog away "solving problems," always with a grim eye on retrieving sunk costs.
I go outside and stand in the cold, smoking a cigarette, under the grim eye of the Wehrmacht eagles watching from our World War II-era barracks.
It would be easy, of course, to cast a grim, funereal eye over the terrain covered by Mr. Hodge, the Scottish screenwriter ("Trainspotting," "Shallow Grave") who with this production marks his theater debut via a topic he intended first for celluloid.
The two of us make a grim, silent eye pact to do what we can to save it, or at least make it more comfortable dying.
At Telluride fest, two films cast grim eye on Mideast.
Mr. Littleton returned to his truck and clipped Mr. Borbon's mug shot — slicked-back hair, a salt-and-pepper moustache, grim eyes with dark circles underneath — onto his sun visor.
The last of these institutions were shut down in 1996, and Peter Mullan's grim, eye-opening drama about them is well worth taping or staying up late for.
Losing bin Laden: How Bill Clinton's Failures Unleashed Global Terror by Richard Miniter (Regnery, $27.95 chronicless in grim, eye-popping detail how the Clinton Administration mortally bungled our pre-9/11 efforts against global terrorism.
Geoffrey Croft of Park Advocates charts such inequities with a grim accountant's eye for detail.
