Dimension reduction is critical for many database and data mining applications, such as efficient storage and retrieval of high-dimensional data. In the literature, a well-known dimension reduction scheme is Linear Discriminant Analysis (LDA). The common aspect of previously proposed LDA based algorithms is the use of Singular Value Decomposition (SVD). Due to the difficulty of designing an incremental solution for the eigenvalue problem on the product of scatter matrices in LDA, there is little work on designing incremental LDA algorithms. In this paper, we propose an LDA based incremental dimension reduction algorithm, called IDR/QR, which applies QR Decomposition rather than SVD. Unlike other LDA based algorithms, this algorithm does not require the whole data matrix in main memory. This is desirable for large data sets. More importantly, with the insertion of new data items, the IDR/QR algorithm can constrain the computational cost by applying efficient QR-updating techniques. Finally, we evaluate the effectiveness of the IDR/QR algorithm in terms of classification accuracy on the reduced dimensional space. Our experiments on several real-world data sets reveal that the accuracy achieved by the IDR/QR algorithm is very close to the best possible accuracy achieved by other LDA based algorithms. However, the IDR/QR algorithm has much less computational cost, especially when new data items are dynamically inserted.