In this paper, we propose a new method for indexing large amounts of points in high-dimensional space. The basic principle is as follows: Data points or feature vectors extracted from objects are first quantized into lattice points by using lattice vector quantization. Inverted file is adopted to organize those lattice points. Fast retrieval is implemented by sing the good properties of algebraic lattice. We first tested the indexing performance for range query by using lattice Eg and Hash. The initial experimental result show our method has good indexing performance. However, we found, Hash has to search the inverted file for a large amounts of lattice points if query window is bigger or dimension is high. To solve this problem, we use Trie instead of Hash and propose Tire Parallel Search Algorithm to fast access the inverted file. Further experiments have been done for n-dimensional data point by using lattice Zn. The results show the proposed index structure owns many good properties such as low CPU cost and low I/O cost in comparison to R-tree.