A fast motion estimation algorithm is proposed, which performs a tree-structured motion vector search for variable blocks in the integer-pixel unit. The proposed method is based on the inequality of sum norms to find the best estimate of the motion vectors for variable blocks. The proposed motion estimation algorithm is applied to the Joint Video Team (JVT) encoder that performs variable-block motion estimation (ME) with quarter-pixel unit. In terms of computational complexity, the proposed motion estimation algorithm searches motion vectors about 10.7 times as fast as the spiral full search with early termination and 6.6 times as fast as the fast full search using the hierarchical sum of absolute difference (SAD), while the PSNR (peak signal-to-noise ratio) of the reconstructed image is slightly degraded.