In recent years, cloud computing is becoming an attractive research topic for its emerging issues and challenges. Not only in research but also the enterprises are rapidly adopting cloud computing because of its numerous profitable services. Cloud computing provides a variety of quality of services (QoSs) and allows its users to access these services in the form of infrastructure, platform and software on a subscription basis. However, due to its flexible nature and huge benefits, the demand for cloud computing is rising day by day. As a circumstance, many cloud service providers (CSPs) have been providing services in the cloud market. Therefore, it becomes significantly cumbersome for cloud users to select an appropriate CSP, especially considering various QoS criteria. This paper presents a hybrid multi-criteria decision-making (H-MCDM) algorithm to find a solution by considering different conflicting QoS criteria. The proposed algorithm takes advantage of two well-known MCDM algorithms, namely analytic network process (ANP) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), to select the best CSP or alternative. Here, ANP is used to categorize the criteria into subnets and finds the local rank of the CSPs in each subnet, followed by VIKOR, to find the global rank of the CSPs. H-MCDM considers both beneficial and non-beneficial criteria and finds the CSP that holds the maximum and minimum values of these criteria, respectively. We demonstrate the performance of H-MCDM using a real-life test case (case study) and compare the results to show the efficacy. Finally, we perform a sensitivity analysis to show the robustness and stability of our algorithm.