Rovio Entertainment Ltd., the Finnish maker of “Angry Birds,” said it is looking to lay off up to nearly 10% of its staff as part of a broader effort to focus on mobile games.

The cuts, which would impact up to 35 of its more than 400 employees, would affect its animation unit as well as support functions and management, while the company’s game divisions wouldn’t be touched, said Kaisu Karvala, a spokeswoman for Rovio.

Employee...