In rapid changing the global business environment, information communication technology (ICT) is essential for the survival of a firm, and the functions of ICT is becoming increasingly important. The emergence of cloud computing represents a fundamental change of ICT services and cloud services continue to grow rapidly with increasing functionality and more users. As a result of this growth, it is a critical issue to select a suitable cloud service which meets all the business strategies and the objectives of firms. This paper proposes a hybrid multi-criteria decision-making model for a cloud service selection problem using balanced scorecard (BSC), fuzzy Delphi method (FDM) and fuzzy analytical hierarchy process (FAHP). We focus on selecting an IaaS among cloud services for firms' users. The BSC concept is applied to define the hierarchy with four major perspectives (i.e. financial, customer, internal business process, and learning and growth), and to derive decision-making criteria and decision-making factors are selected for each BSC perspective. FDM is used to select the list of important decisionmaking factors within each BSC perspective based on the decision makers' opinion. A FAHP approach is then proposed in order to compares the decision-making criteria and factors and determine the importance of them. It is also used to select the best cloud service among the cloud service alternatives based on the predetermined weights of decisionmaking criteria and factors. In this study, the BSC and FAHP as the hybrid multi-criteria decision-making technique are used to select the best cloud service. Our findings can be utilized as bases to apply systematic decision-making processes for the best cloud service selection and for providing guidance to IT department managers or CTO regarding performance evaluation and strategies to improve companies' performance and capability.