  A quark confinement potential is derived from QCD Lagrangial under the two
assumptions in the energy region relevant to quark confinement. The possibility
of perturbation in QCD is assumed, and the momentum of the gluon transfered by
the quark is larger than the mass of the internal quark, so that the expansion
of ${m^2 /{q^2}}$ is assumed to be reliable. This potential comes from the one
loop diagrams in the expansion of $m^2 /{q^2}$, especially here, the vacuum
polarization diagram is examined. This explains the quark confinement mechanism
on the basis of QCD and the Regge trajectories which is governed by a linear
potential.
