This paper is devoted to the calculation of parity nonconserving (PNC) effects in the diatomic homonuclear molecule of oxygen O₂. For this purpose the magnetic dipole transition bσ_g ⁺ ↔ X³σ_g ^-was considered. It was believed that the weak electron-electron interaction prevails over the weak interaction of electrons with nuclei in this case. This idea appeared not to be justified for molecular oxygen. As it turns out from our calculations, the parity nonconservation degree for the weak electron-nucleus interaction is of the order P^eN =1.4 .10^-11and for the weak electron-electron interaction is by two orders smaller P^eN = 1.1 10^-13. Nevertheless, a PNC experiment for the observation of the weak electron-nucleus interaction looks sufficiently feasible (previously, such experiments were carried out only with atoms).