Spatio-temporal modeling is one of the most important topics in the field of GIS. Unified representation of space and time can be seen as a new potential for temporal GIS, though practical advices on it in real world are still lack. The geometric algebra linking expression and computation of elements at different dimensions provides potations to express space and time in a unified framework. This paper proposes geometric algebra to overcome the drawbacks of existing vector spatio-temporal data modeling methods in representing time and space individually, which will lead to express inconsistent and not uniform issue. Based on the coding of coordinates with geometric algebra elements, the unified spatio-temporal expression integrates the temporal and spatial parts as a whole, by linking the basic elements of geometric algebra of different grades. And then, time, space and attributes are expressed and modeled based on geometric algebra and unified spatial-temporal views. The heretical level structure of unified spatio-temporal expression is proposed and the logical relations of time, space and attributes are discussed based on the UML technology in an object-oriented way. The process flow of unified vector spatio-temporal data model was proposed. Based on the multivector structure of geometric algebra, data organization and storage structures were defined. Finally, a prototype system was implemented that integrates the above mentioned technologies. Changing data of administrative regions (at prefectural level) of southeast China was used to evaluate the method. The results suggest that the method proposed in this paper can support unified spatio-temporal modeling and expression, which can also support the construction and implementation of spatio-temporal analysis methods, e.g. change detection. It seems that our work can provide theoretical foundation and method implementation reference for the development of temporal and spatial GIS.