It is shown that the potential model constructed by the one-gluon exchange interaction plus the scalar linear potential cannot well explain the splittings of P states of heavy quarkonium in this note. However, if the model is modified by the hypothesis that the Lorentz structure of confinement is expressed by a combination of five independent Lorentz invariants, such as scalar, pseudoscalar, vector, axial-vector and tensor-type couplings, we find that the model is able to reproduce almost all the features of the P-state splittings for the cc system.