Cloud is a relatively new concept and so it is unsurprising that the information assurance, data protection, network security and privacy concerns have yet to be fully addressed. The cloud allows users to avoid upfront hardware and software investments, gain flexibility, collaborate with others, and take advantage of the sophisticated services. However, security is a huge issue for cloud users especially access control, user profile management and accessing services offered by the private cloud environment. A privacy enhancement system on Academic-based private cloud system using Eucalyptus open source cloud infrastructure has been proposed in this paper. This system provides the cloud users to improve the privacy and security of the private personal data. Two approaches (Role-based Access Control and Attribute-based Access Control model) are combined as a new approach (ARBAC). This means that they are applied to improve the privacy which supports both mandatory and discretionary access control needs on the target private cloud system.