The potential energy curves for six electronic states, X2∑+，Ａ2∏i，Ｂ2∑+，Ｃ2∏i，Ｄ2∑+ and Ｅ2∏r of the linear ArCN molecule have been calculated at the ROHF level with the 6-31G* and 6-31G?* basis sets, respectively. The calculation (ROHF) results for the electronic states of ArCN indicate that it is an exciplex. The UHF calculations for the X2∑+ and Ａ2∏i states demonstrate that big spin contaminations in the UHF wavefunctions do not influence the shapes of these two potential energy curves.