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In the context of the dual superconductor picture for the confinementmechanism, we study maximally Abelian (MA) projection of quark confinement inSU(3) quenched lattice QCD with $32^4$ at $\beta$=6.4 (i.e., $a \simeq$ 0.058fm). We investigate the static quark-antiquark potential $V(r)$, its Abelianpart $V_{\rm Abel}(r)$ and its off-diagonal part $V_{\rm off}(r)$,respectively, from the on-axis lattice data. As a remarkable fact, we findalmost perfect Abelian dominance for quark confinement, i.e., $\sigma_{\rmAbel} \simeq \sigma$ for the string tension, on the fine and large-volumelattice. We find also a nontrivial summation relation of $V(r) \simeq V_{\rmAbel}(r) + V_{\rm off}(r)$.

Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD