Process capability indices(PCIs), whose purpose is to provide a numerical measure on whether a production process is capable of producing items that satisfy the quality requirement preset by the customers, have received substantial research attention. Most research work, however, have focused on developing and investigating PCIs for processes with symmetric tolerances. PCIs for populations with asymmetric tolerances have been comparatively neglected. Recently, Boyles[2] reviewed several existing PCIs and proposed four new indices to handle populations with asymmetric tolerances. Unfortunately, those indices do not reflect process capability accurate enough. In this paper, we propose a new capability index so that positive uses of PCIs can be continued. The proposed new index is compared with the existing PCIs in terms of a process characteristic discussed in Choi and Owen [4]. The results indicated that the new index reflect process capability more accurately than the existing ones.