Customer relationships have been commonly recognized as a critical factor for enterprises to succeed their business. Effective customer relationships could help enterprises deliver services to customers based on their needs, preferences, or past transactions. This model however emphasizes on the use of customer information for benefiting enterprises; customers in contrast receive less information from enterprises. To address this issue, the paradigm Consumer Support Systems (CSS) is proposed to support the provision of service information for customers to help on their decision making. In addition, since Cloud Computing has been popularity for its rich set of features and their practical applications on business can be expected, it is thus an envisioned trend for CSS to be deployed on clouds to enhance further its effectiveness on customer relationships. For this need, we present in this paper a cloud deployment approach for such a cloud-based CSS. The approach starts from the consideration of CSS and cloud characteristics, through the recognition of the architectural components in CSS and clouds, and finally ends with the deployment of the architectural components in CSS on clouds. The approach is illustrated by a cloud-based CSS for travel arrangement where decision support for travels is provided for satisfying the arrangement needs from travelers.