Both quark-confinement and chiral symmetry breaking are important non-perturbative phenomena in low-energy QCD. The motivation in this study is to investigate the relation between them. To that end, we derive some analytical relations between the Polyakov loop and the eigenmodes of the Dirac operator on a lattice. Those formulae suggest no direct one-to-one correspondence between quark-confinement and chiral symmtery breaking in QCD.