We show the construction of the dual superconducting theory fur the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared albelian dominance is naturally understood with the off-diagonal gluon mass m(off) similar or equal to 1.2GeV induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase: tends tu be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-diagonal gluon phase leads to abelian dominance for the string tension. In the MA gauge, there appears the macroscopic network of thr: monopole world-line: covering the whole system. We investigate the monopole-current system in the MA gauge by analyzing the dual gluon field B-mu. We evaluate the dual gluon mass as m(B) = 0.4 similar to 0.5GeV in the infrared region, which is the lattice-QCD evidence of the: dual Higgs mechanism by monopole condensation. Owing to infrared abelian dominance and infrared monopole condensation, QCD ill the MA gauge is describable with the dual Ginzburg-Landau theory.