Cyber space is affecting all areas of our life. Cloud computing is the cutting-edge technology of this cyber space and has established itself as one of the most important resources sharing technologies for future on-demand services and infrastructures that support Internet of Things (IOTs), big data platforms and software-defined systems/services. More than ever, security is vital for cloud environment. There exist several cloud security models and standards dealing with emerging cloud security threats. However, these models are mostly reactive rather than proactive and they do not provide adequate measures to assess the overall security status of a cloud system. Out of existing models, capability maturity models, which have been used by many organizations, offer a realistic approach to address these problems using management by security domains and security assessment on maturity levels. The aim of the paper is twofold: first, it provides a review of capability maturity models and security metrics; second, it proposes a cloud security capability maturity model (CSCMM) that extends existing cyber security models with a security metric framework.