  We study the Calabi-Yau property of pointed Hopf algebra $U(\mc{D},\lmd)$ of
finite Cartan type. It turns out that this class of pointed Hopf algebras
constructed by N. Andruskiewitsch and H.-J. Schneider contains many Calabi-Yau
Hopf algebras. To give concrete examples of new Calabi-Yau Hopf algebras, we
classify the Calabi-Yau pointed Hopf algebras $U(\mc{D},\lmd)$ of dimension
less than 5.
