  We investigate gluon propagators and the effective mass of the gluon fields
in the MA gauge with U(1)$_3 \times$ U(1)$_8$ Landau gauge fixing in SU(3)
lattice QCD. The Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7,
5.8 and 6.0 and $32^4$ at $\beta=$5.8 and 6.0 at the quenched level. To
calculate the propagators, we adopt a method to extract gauge fields from
link-variables analytically in the SU(3) case. The off-diagonal gluons behave
as massive vector bosons with the approximate effective mass $M_{\rm off}
\simeq 1.1 - 1.2 {\rm GeV}$ in the region of $r = 0.3 - 0.8 {\rm fm}$, and the
propagation is limited within a short range. On the other hand, the diagonal
gluons behave as light vector bosons with $M_{\rm diag}\simeq 0.3 {\rm GeV} $
and the propagation of diagonal gluons remains even in a large range. In this
way, infrared Abelian dominance is shown in terms of short-range propagation of
off-diagonal gluons. Furthermore, we investigate the functional form of the
off-diagonal gluon propagator. The functional form is well described by the
four-dimensional Euclidean Yukawa-type function ${\rm exp}(-m_{\rm off} r)/r$
with $m_{\rm off} = 1.3 -1.4 {\rm GeV}$ for $r = 0.1- 0.8{\rm fm}$. This also
indicates that the spectral function of off-diagonal gluons has the
negative-value region.
