Miyori no Mori

Also known as:  Miyori's Forest, Miyori's Wood

After being deserted by her parents, 11-year old Miyori shuts her heart from the rest of the world and denies any form of human relationships. She is placed in the care of her grandmother, who lives near a forest. As Miyori takes a walk in the forest, she feels a strong sense of loneliness, but soon she encounters unbelievable things and gradually realizes that the forest is more than what it seems... (based on ANN synopsis)

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Producers, official website and other details: AniDB, ANN, Wiki