The contribution of two-pion exchange three-body force from the P-wave π-N scattering to the binding energy of nuclear matter is investigated. The three-body force (TBF) is derived as the effective two-body force under consideration of the correlations between all the pairs of nucleons concerned with TBF. The reaction-matrix equations are solved self-consistently with two- and three-(effective two-) body potenial. The binding energy contribution from TBF is about 3.5 MeV attraction for the case of the Hamada-Johnston potential and 4.1 MeV for Tamagaki's OPEH potential. The characteristic effect of TBF is discussed in connection with the binding energy and the saturation density. In nuclear matter calculation with two-nucleon potentials, there seems to be that the energy gain has generally been accompanied by increasing the saturation density, but our results show that TBF gives the energy gain, but does not increase the saturation density so much as two-body force does.