  Motivated by one-dimensional color-electric flux-tube formation in
four-dimensional (4D) QCD, we investigate a possibility of effective
dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge
fixing of "dimensional reduction (DR) gauge" defined so as to minimize
$R_{\mathrm{DR}}~\equiv~\int d^{4}s ~ \mathrm{Tr} \left[ A_{x}^{2}(s) +
A_{y}^{2}(s) \right]$, which has a residual gauge symmetry for the gauge
function $\Omega (t,z)$ like 2D QCD on the $t$-$z$ plane. We investigate
effective dimensional reduction in the DR gauge using SU(3) quenched lattice
QCD at $\beta = 6.0$. The amplitude of $A_{x}(s)$ and $A_{y}(s)$ are found to
be strongly suppressed in the DR gauge. We consider "$tz$-projection" of
$A_{x,y}(s) \to 0$ for the gauge configuration generated in the DR gauge, in a
similar sense to Abelian projection in the maximally Abelian gauge. By the
$tz$-projection in the DR gauge, the interquark potential is not changed, and
$A_{t}(s)$ and $A_{z}(s)$ play a dominant role in quark confinement. In the DR
gauge, we calculate a spatial correlation $\langle \mathrm{Tr} A_{\perp}(s)
A_{\perp}(s+ra_{\perp}) \rangle ~ (\perp = x,y)$ and estimate the spatial mass
of $A_{\perp}(s) ~ (\perp = x,y)$ as $M \simeq 1.7 ~ \mathrm{GeV}$. It is
conjectured that this large mass makes $A_{\perp}(s)$ inactive and realizes the
dominance of $A_{t}(s)$ and $A_{z}(s)$ in infrared region in the DR gauge. We
also calculate the spatial correlation of two temporal link-variables and find
that the correlation decreases as $\exp (-mr)$ with $m \simeq 0.6 ~
\mathrm{GeV}$. Using a crude approximation, the 4D YM theory is reduced into an
ensemble of 2D YM systems with the coupling of $g_{\rm 2D} = g m$.
