By using CRM, the organization will be able to identify of what customer requires and needs, thus will improve the service. The designing of CRM the Computer Science Department using Zachman Framework is one of the approach methods that can describe a more complex and thorough system information design. Zachman Framework has not provided a method for determining the priority of the application candidates that will be designed. Even though there are several methods to determine the priority of candidates of the information system, in this research the authors use the Ward and Peppard’s composite matrix portfolio and business process analysis for priority to determine the priority of application candidates. The phase of candidates determination by using Ward and Peppard’s composite matrix and business process is the identification of information related to Computer Science Department, SWOT analysis, business process and value chain analysis, the analysis of ISO 9001:2008 quality procedure implementation related to customer, the determination of application’s candidate, and the implementation of the questionnaire mapping of application candidate. The results are in the form of mapping for each application candidate/application system into four quadrants which are provided in composite matrix for the decision-making process. The matrix consists of key operational, strategic, high potential and support. The mapping of application candidate/information system is suitable with the contribution of each information system toward the CRM in Computer Science Department, University of Lampung. The mapping on Ward and Peppard’s composite matrix is then used to separate the application candidates into two groups, the main priority of application group/information system and non-main priority of application group/information system. There are five information systems which are classified into main priority application group/information system and recommended to be developed in further research.