All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is permissible to feed this big fish with some small fish, but you should not give them to it while they are still alive, as this may be a sort of punishment to these small fish. Therefore, you should first kill these small fish before giving them as food for the big fish, as the Prophet said: "Verily, Allaah has prescribed Al-Ihsaan (i.e. performing an action in a perfect and kind manner) towards everything. Thus, if you kill (anyone for some justified reason), kill (him/her) humanely; when you slaughter (an animal), slaughter (it) well. And everyone of you should sharpen his blade to avoid torturing the animal he slaughters." [Muslim]
For more benefit, please refer to Fataawa 89700 and 88818.
Allaah Knows best.