"grave look" is correct and usable in written English.
You can use it to describe someone's facial expression when they are looking serious or apprehensive. Example: The teacher gave us a grave look as we entered the classroom late.
"Haven't seem them," says the youngest one, fixing me with a grave look.
With a grave look on his face, Frank instructs me to tell him when I feel a tingling.
"There's a real effort to get people from cradle to grave — look at the Met's new education center".
His father's pause, his grave look, his utter attention: "If I were a millionaire, I would pay for the privilege of teaching".
When adults are talking about skateboarding, he stands right underneath them and tips one ear up toward them with a grave look on his face.
Bob turned to me and, with a grave look, said, "I think I should tell you that I'm a Republican and I support McCain".
Hannah stood alone near the grave, looking uncomfortable, but next to her the elderly prophetess was smiling.
There's no obvious path up from the road, so we climbed through the grass and found the grave looking not obscure but unvisited.
There she is, in a wheelchair, holding baby Lorenzo Dominic, her expression composed, dignified, almost grave, looking straight ahead, as if into her mom future.
Party officials paid for Mr. Malunga's burial, and his brick and stucco grave looks lavish next to the unadorned earthen mounds in the family graveyard that hold his father, brother and nephew.
Some of the kids who protested were very young, as young as the kids who had been killed five years before at Sandy Hook, and almost all of them had grave looks on their faces as they held up their signs.
