Gaki Jigoku

On a stormy night, twin sisters are born. One of the girls is healthy and normal in every regard - the other is hideously deformed and craves blood rather than milk. The father of the girls is unwilling to accept the deformed twin into his family and so he places her in a sack and disposes of her at a rubbish dump. The baby subsists first on carrion and earthworms and then, later, by hunting the dogs, rats, crows and other animals that inhabit the dump (something she must do regularly since she begins to decompose when she doesn't get a regular supply of blood). After seven years, she leaves the dump and heads for the distant lights of the city - there she will discover that human blood tastes best of all and maybe find out something about the family that abandoned her.
(Source: Anime News Network)