Many organizations are currently seeking to contract services from cloud computing rather than owing the possessions to supply those services. Due to the fast expansion of cloud computing, many cloud services have been developed. Any organization that tries to achieve the best flexibility and quick response to market requests, they have the options to use cloud services. Due to the diversity of cloud service providers, it is a very significant defy for organizations to select the appropriate cloud services which can fulfill their requirements, as numerous criteria should be counted in the selection process of cloud services. Therefore, the selection process of cloud services can be considered as a type of multi-criteria decision analysis problems. In this research paper, we present how to aid a decision maker to estimate different cloud services by providing a neutrosophic multi-criteria decision analysis (NMCDA) approach for estimating the quality of cloud services. Triangular neutrosophic numbers are used to deal with ambiguous and incompatible information which exist usually in the performance estimation process. An efficacious model is evolved depending on neutrosophic analytic hierarchy process (NAHP). The aim is to solve the performance estimation problem and improve the quality of services by creating a strong competition between cloud providers. To demonstrate the pertinence of the proposed model for disbanding the multi-criteria decision analysis, a case study is presented.