Temporal index is one of key technologies for temporal data managements. This paper discusses a temporal data structure and its application for temporal data index. Most of existing temporal data methods are based on algebra framework. This paper presents a temporal data structure using quasi-order relation which can achieve multithreading data operations, and puts forward temporal index TQOindex supported by the structure. Firstly, it proposes the conception of quasi-order relationship of temporal data and studies the construct algorithm of linear order partition and its optimal property. Secondly, it dedicates application on temporal data structure with building TQOindex on expand quasi-order set which manages data on disks and can be used in common databases platform. TQOindex can dynamically index "big data" by its querying schema of "one time, one set" as well as incremental update mechanism. Finally, the simulations in the paper show the feasibility and validity for TQOindex. In conclusion, temporal quasi-order data structure pays attention to the mechanism of the processing and integration between time and application scene information for new kinds of data such as semantic data, XML data and moving objects data, and the works in this paper offers remarkable extendibility.