Characteristic features of the positron binding structure of some nitrile (–CN functional group) species such as acetonitrile, cyanoacetylene, acrylonitrile, and propionitrile are discussed with the configuration interaction scheme of multi-component molecular orbital calculations. This method can take the electron–positron correlation contribution into account through single electronic–single positronic excitation configurations. Our PA value of acetonitrile with the electronic 6-31++G(2df,2pd) and positronic [15s15p3d2f1g] basis set is calculated as 4.96 mhartree, which agrees to within 25% with the recent experimental value of 6.6 mhartree by Danielson et al. [Phys. Rev. Lett., 2010, 104, 233201]. Our PA values of acrylonitrile and propionitrile (5.70 and 6.04 mhartree) are the largest among these species, which is consistent with the relatively large dipole moments of the latter two systems.