The problems of evaluating Telecommunication Management Network Operation Systems (TMNOS) are Multi-Criteria Decision Making (MCDM) problems. A method for evaluating the TMNOS has not yet been clearly defined. A study of an effective and efficient management methodology for TMNOS, which are heterogeneous and complex, is needed. The components of TMNOS have attributes of dependence between considered criteria or alternatives. This type of dependence impact between criteria or alternatives is a network structure. We suggest a methodology of Analytic Delphi Network Process (ADNP) for evaluating TMONS. The TMNOS problem of Korea Telecom (KT) is suggested as a case study of the ADNP.