The fast emergence of the cloud based computation fulfills modern telecommunication serve firms' requirements for massive computation and storage space with very low costs. However, how the cloud-based service quality can be enhanced, how customers' needs can be fulfilled, and how firms' profits can be maximized were seldom discussed. Thus, this research aims to provide a new hybrid MCDM model combining DEMATEL and ANP based framework and Grey Relational Analysis (GRA) for improving to close the service quality gap, fulfill customers' satisfactory and maximize profits in interdependence and feedback problems among dimensions/criteria. An empirical case study bases on enhancing the service quality of a Taiwanese mobile telecommunication firm's application of cloud computation as the billing system. In results of this case study, the expertise in dynamic capacity management and new education and training should be the most important strategies for service quality enhancement to be introduced.