This paper addresses the problem of determining trustworthiness of Cloud Service Providers (CSPs) in a cloud environment. For the current work, trustworthiness is defined as the degree of compliance of a CSP to the promised quantitative QoS parameters as defined in the Service Level Agreement (SLA). Due to large number of CSPs offering similar kinds of services in the cloud environment, it has become a challenging task for Cloud Clients (CCs) to identify and differentiate between the trustworthy and untrustworthy CSPs. At present, there is no trust evaluation system that allows CCs to evaluate the trustworthiness of CSPs on the basis of their adherence to the SLA i.e. the compliance provided by the CSPs to CCs as per the SLAs. This paper proposes a Compliance-based Multi-dimensional Trust Evaluation System (CMTES) that enables CCs to determine the trustworthiness of a CSP from different perspectives, as trust is a subjective concept. Such a system is of great help to CCs who want to choose a CSP from a pool of CSPs, satisfying their desired QoS requirements. The framework enables us to evaluate the trustworthiness of a CSP from the CC’s perspective, Cloud Auditor’s perspective, Cloud Broker’s perspective and Peers’ perspective. Experimental results show that the CMTES is effective and stable in differentiating trustworthy and untrustworthy CSPs. The validation of the CMTES has been done with the help of synthetic data due to lack of standardized dataset and its applicability has been demonstrated with the help of a case study involving the use of real cloud data. •The paper presents a compliance-based multi-dimensional trust evaluation system (CMTES).•CMTES supports evaluation of trustworthiness from the viewpoint of various stakeholders like Cloud Auditor, Peers and Cloud Broker, etc.•CMTES uses Improved TOPSIS technique to derive trustworthiness from compliance values.•Mathematical descriptions supporting CMTES have been provided.•The strategy has been simulated using synthetic as well as real cloud data.