The quality offered by cloud computing services is becoming an issue of the utmost priority and, regardless of the cloud delivery models, the adoption of cloud services will depend on having the capability to ensure quality of service to the users. However, studies to find and select cloud computing services according to their service quality are still in their infancy. Here, we propose a system that calculates the priority weights for each quality attribute according to the quality preference of a user and the interrelation analysis results between the attributes, and reflects the weights in selecting the cloud computing service. To calculate the quality preference of the user, we applied a pairwise comparison matrix and an eigenvector of the matrix. Through the proposed system, users can easily perform the process of calculating the weights and selecting the best services according to their quality preference. The simulation results show that the weights of the quality attributes and the quality score ranking of the sample cloud computing services vary according to users’ preferences and interrelations between attributes.