In the leading O(α 4 s ) order of the perturbative QCD, the hadronic production cross-sections of S-and P -wave states of B c meson are calculated. The results for the S-wave levels are compared with the values given in other papers as well as in the model of the b quark fragmenatation into B c . In the given order, the crosssections of the hadronic production of the P -wave states are calculated for the first time. Their contribution into the B c meson production is less than 10%. There is a strong difference between the predictions of the fragmentation model and the exact perturbative calculations. These difeerences are discussed in details for the differential distributions over variuos kinematical quantities.