The vibrational cross sections of the CO molecule induced by positron impact is the focus of this work. The positron–molecule interaction is represented by the static potential plus a model potential designed to take into account the positron–target correlations. To calculate the vibrational cross sections, we applied the multichannel version of the continued fractions method in the close-coupling scheme. We present vibrational excitation cross sections and elastic ones, for the ground and excited vibrational states. The results are interpreted in terms of the vibrational coupling-scheme used in the scattering model.