The cloud computing immerges as a new computing technology where all required services are available as a service. In a cloud environment, location of data is generally maintained by a third party (service provider/vendor) and hence an individual has no control over its own data. In this context, data privacy is an important issue for cloud computing both in terms of legal compliance and user trust. In this paper, an approach for data privacy in hybrid cloud environment is focused. Initially, a data privacy model for cloud computing is provided in which sensitive and non-sensitive data are maintained separately. In order to maintain data privacy, an authentication monitor is introduced in this privacy model. Finally, the authentication algorithm is implemented in a very small setup cloud environment and experimental results are provided at the end of the paper.