In this paper, we propose a computation scheme to reduce computational complexities of the discrete cosine transform (DCT) and quantization. Based on the relationship between block contents and the quantization table, the end-of-block (EOB) point is predicted in the 2-dimensional 8x8 DCT computation structure for the H.263 video encoder. Using the predicted EOB point, the DCT calculation structure is minimized and the number of points required for quantization is also decreased. The top-down, binary-tree and bottom-up techniques of searching the EOB point are explored where the adequate searching points are utilized to minimize the truncation error of the DCT computation structure. As compared to the fixed 32-coefficient and 64-coefficient DCT schemes, the proposed scheme takes the least computational complexity. The quality of the decoded video using the proposed scheme is better than that using the 32-coefficient DCT scheme and close to that using the 64-coefficient DCT scheme. Therefore, the computation scheme proposed herein can be widely utilized in video and image compression applications.