We have studied alpha-induction, which is a certain machinery to deal with induced representations for a braided fusion category, from a viewpoint of bi-unitary connections. Alpha-induction is a tensor functor arising from a (not necessarily commutative) Frobenius algebra in a braided fusion category, and it has been studied as an extension of endomorphisms of a subfactor of type III to a larger factor. It is also known in subfactor theory of operator algebras that a family of unitary matrices called connections describe a fusion category. We have clarified how to describe alpha-induction for a braided fusion category given by connections. In particular, we have shown that if a Frobenius algebra is commutative, then the alpha-induced connection is flat.