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The dual superconductivity is a promising mechanism for quark confinement. Wehave proposed the non-Abelian dual superconductivity picture for SU(3)Yang-Mills theory, and showed the restricted field dominance (calledconventionally Abelian dominance), and non-Abelian magnetic monopole dominancein the string tension. We have further demonstrated by measuring thechromoelectric flux that the non-Abelian dual Meissner effect exists anddetermined that the dual superconductivity for SU(3) case is of type I, whichis in sharp contrast to the SU(2) case: the border of type I and type II.  In this talk, we focus on the confinement/deconfinement phase transition andthe non-Abelian dual superconductivity at a finite temperature: We measure thePolyakov loop average and correlator and investigate the restricted fielddominance in the Polyakov loop. Then, we measure the chromoelectric fluxbetween a pair of static quark and antiquark created by a pair of Polyakovloops, and investigate the non-Abelian dual Meissner effect and its relevanceto the phase transition.

Non-Abelian dual Meissner effect in SU(3) Yang-Mills theory and confinement/deconfinement phase transition at finite temperature