  In this paper we construct Mabuchi $\mathcal{L}^{{\rm M}}_{\omega}$
functional and Aubin-Yau functionals $\mathcal{I}^{{\rm AY}}_{\omega},
\mathcal{J}^{{\rm AY}}_{\omega}$ on any compact complex three-folds. The method
presented here will be used in the forthcoming paper \cite{L1} on the
construction of those functionals on any compact complex manifolds, which
generalizes the previous work \cite{L}.
