In this study, we propose a novel vector quantization algorithm for Approximate Nearest Neighbor (ANN) search, based on a joint competitive learning strategy and hence called as competitive quantization (CompQ). CompQ is a hierarchical algorithm, which iteratively minimizes the quantization error by jointly optimizing the codebooks in each layer, using a gradient decent approach. An extensive set of experimental results and comparative evaluations show that CompQ outperforms the-state-of-the-art while retaining a comparable computational complexity.