  A new general parameterization with eight mixing parameters among Z, gamma
and an extra neutral gauge boson Z' is proposed and subjected to
phenomenological analysis. We show that in addition to the conventional
Weinberg angle theta_W, there are seven other phenomenological parameters G',
xi, eta, theta_l, theta_r, r, l for the most general Z-gamma-Z' mixings, in
which parameter G' arises due to the presence of an extra Stueckelberg-type
mass coupling. Combined with the conventional Z-Z' mass mixing angle theta',
the remaining six parameters xi, eta, theta_l-theta', theta_r-theta', r, l are
caused by general kinetic mixings. In all the eight phenomenological parameters
theta_W, G', xi, eta, theta_l, theta_r, r, l, we can determine the Z-Z' mass
mixing angle theta' and the mass ratio M_Z/M_Z'. The Z-gamma-Z' mixings we
discuss are based on the model-independent description of the extended
electroweak chiral Lagrangian (EWCL) previous proposed by us. In addition, we
show that there are eight corresponding independent theoretical coefficients in
our EWCL which are fully fixed by our eight phenomenological mixing parameters.
We further find that the experimental measurability of these eight parameters
does not rely on the extended neutral current for Z', but depends on the Z-Z'
mass ratio.
