High-dimensional indexing has been very popularly used for performing similarity search over various data types such as multimedia (audio/image/video) databases, document collections, time-series data, sensor data and scientific databases. Because of the curse of dimensionality, it is already known that well-known data structures like kd-tree, R-tree, and M-tree suffer in their performance over high-dimensional data space which is inferior to a brute-force approach linear scan. In this paper, we focus on an approximate nearest neighbor search for two different types of queries: r-Range search and k-NN search. Adapting a novel concept of a ring structure, we define a new index structure MLR-Index (Multi-Layer Ring-based Index) in a metric space and propose time and space efficient algorithms with high accuracy. Evaluations through comprehensive experiments comparing with the best-known high-dimensional indexing method LSH show that our approach is faster for a similar accuracy, and shows higher accuracy for a similar response time than LSH.