The article constructs TSM Tree storage model for big data stream, optimizes the fast query method by using APSO algorithm thinking, and constructs fast query model for big data stream by using discrete wavelet transform. The storage and retrieval performance of the big data stream storage model and fast query model are verified respectively.The TSM Tree storage model has high storage efficiency. The storage rate of the TSM Tree storage model increases rapidly when the file size is larger than 20MB, and the TSM Tree storage model is suitable for storing big data files over 20MB. In this paper, the fast indexing method has the highest Put execution efficiency and becomes the secondary indexing method for single condition query. The fast indexing method in this paper is optimized on multi-conditional query with the fastest response time of 0.954, 0.898, and 0.907s.