We apply the method of the QCD sum rule, in which positive- and negative-parity baryons couple with each other, to the flavor-octet baryons and investigate the parity splittings. The obtained sum rules turn out to have a very good Borel stability and also have a Borel window. The predicted masses of the positive- and negative-parity baryons reproduce the experimental ones fairly well in the Λ and Σ channels, if we assign the Λ(1670) and the Σ(1620) to the parity partners of the Λ and the Σ, respectively. This implies that the Λ(1405) is not the party partner of the Λ and may be a flavor-singlet or exotic state. In the Ξ channel, the sum rule predicts the mass of the negative-parity state to be about 1.8~GeV, which leads to two possibilities; one is that the observed state, Ξ(1690), is the parity partner and the other is that the parity partner is not yet found but exists around 1.8~GeV.