  A new parafermionic algebra associated with the homogeneous space
$A^{(2)}_2/U(1)$ and its corresponding $Z$-algebra have been recently proposed.
In this paper, we give a free boson representation of the $A^{(2)}_2$
parafermion algebra in terms of seven free fields. Free field realizations of
the parafermionic energy-momentum tensor and screening currents are also
obtained. A new algebraic structure is discovered, which contains a $W$-algebra
type primary field with spin two.
