  A gauge field model, which simultaneously has strict local gauge symmetry and
contains massive general gauge bosons, is discussed in this paper. The model
has SU(N) gauge symmetry. In order to introduce the mass term of gauge fields
directly without violating the gauge symmetry of the theory, two sets of gauge
fields will be introduced into the theory. After some transformations, one set
of gauge fields obtain masses and another set of gauge fields keep massless. In
the limit $\alpha \longrightarrow 0$ or $\alpha \longrightarrow \infty$, the
gauge field model discussed in this paper will return to Yang-Mills gauge field
model. Finally, some applications of this model are discussed.
