Affine Lie algebras are infinite dimensional analogs of finite dimensional simple Lie algebras. It is known there are finitely many maximal dominant weights for any integrable highest weight representation of an affine Lie algebra. However, determining these maximal dominant weights is a nontrivial task. So far only the descriptions of these weights are known for affine Lie algebra A_n^{(1)}. In this talk we will discuss the maximal dominant weights of the integrable highest weight representation of any affine Lie algebra with highest weight kΛ0 and give some examples of their multiplicities.