The answer to your question depends how the kugel is prepared.

Some kugels are made with old challah, which is bread. Challah kugels are most definitely chametz, forbidden on Passover.

Classic noodle kugel is made with egg noodles. Those are also chametz, and are not allowed for the duration of Passover.

Another popular kugel is rice kugel. Now rice is kitniyot, the class of foods which Ashkenazim (and some Sephardim) may not eat on Passover. Read more at Is Rice Kosher for Passover?

Potato kugel, on the other hand, can very easily be made with only kosher-for-Passover ingredients (potato, onion, egg, Passover oil, salt, and pepper). Provided that you made the kugel in a kosher-for-Passover kitchen, you have a delicious Passover feast.