  In this paper, we discuss the Poincar\'{e} series of Kac-Moody Lie algebras,
especially for indefinite type. Firstly, we compute the Poincar\'{e} series of
certain indefinite Kac-Moody Lie algebras whose Cartan matrices have the same
type of $2\times 2$ principal sub-matrices. Secondly, we show that the
Poincar\'{e} series of Kac-Moody Lie algebras satisfy certain interesting
properties. Lastly we give some applications of the Poincar\'{e} series to
other fields. Particularly we construct some counter examples to a conjecture
of Victor Kac\cite{Kac_85} and a conjecture of Chapavalov, Leites and
Stekolshchik\cite{CDR_10}.
