The Water Horse by Dick King-Smith
The story begins with a mysterious egg washed up on a Scottish beach, the morning after a great storm. Kirstie and her brother Angus find the egg and take it home. The next day it has hatched into a tiny greeny-grey creature with a horse's head, warty skin, four flippers and a crocodile's tail. The baby sea monster soon becomes the family pet - but the trouble is, it just doesn't stop growing!