  All one-loop renormalization constants for Non-Abelian gauge theory are
computed in details by using the symmetry-preserving Loop Regularization method
proposed in\cite{LR1,LR2}. The resulting renormalization constants are
manifestly shown to satisfy Ward-Takahaski-Slavnov-Taylor identities, and lead
to the well-known one loop $\beta$ function for Non-Abelian gauge theory of
QCD\cite{GWP}. The loop regularization method is realized in the dimension of
original field theories, it maintains not only symmetries but also divergent
behaviors of original field theories with the introduction of two energy
scales. Such two scales play the roles of characterizing and sliding energy
scales as well as ultraviolet and infrared cutoff energy scales. An explicit
Check of those identities provides a clear demonstration how the
symmetry-preserving Loop Regularization method can consistently be applied to
non-Abelian gauge theories.
